Earth Systems Science · Module 6

What would it take to stand somewhere else?

No one has touched a star. Almost everything we know about space reached Earth as light.

These slides give you the science, math, and data to plan the trip.

Start → Jump to my project Formula sheet
Four destinations, four problems, and how long their light takes to reach us A dot plot on a logarithmic time scale. Light from the Moon reaches Earth in 1.3 seconds, from Mars in 3 to 22 minutes depending on where the two planets are, from Jupiter's moon Europa in 33 to 54 minutes, and from the planet Proxima Centauri b in 4.25 years. Each place is hard in its own way. The Moon's nights last 14.8 days and its ground cools to 95 K. Mars has air at 0.6 percent of Earth's surface pressure and gets 43 percent of Earth's sunlight. Europa sits inside Jupiter's radiation belts, and a spacecraft takes about five and a half years to get there. Proxima Centauri b is 4.25 light-years away, about 75,000 years at Voyager 1's speed. How long their light takes to reach Earth Moon nights last 14.8 days ground cools to 95 K Mars air 0.6% of Earth's pressure 43% of Earth's sunlight Europa (Jupiter) inside Jupiter's radiation belts a 5½-year trip to get there Proxima Centauri b 4.25 light-years away 75,000 yr at Voyager 1's speed 1.3 s 3–22 min 33–54 min 4.25 yr 1 s1 min1 h1 day1 yr light-travel time (log scale)
Every one of these worlds is known to us mostly through the light it sends or reflects.

Start here · The big picture

Zoom out: the Moon, the planets, the stars, the galaxies

Four parts of Module 6, from nearest to farthest Four panels joined by arrows, each farther out than the last. Part 1, Moon Watch: Earth and the Moon, 384,400 kilometres apart. Part 2, Planet Builders: the solar system, with Neptune 30 astronomical units from the Sun. Part 3, Star Lab: the stars, with the nearest, Proxima Centauri, 4.25 light-years away. Part 4, Galaxy Mappers: galaxies, with the Milky Way about 100,000 light-years across. 384,400 km Earth & Moon Part 1 Moon Watch Neptune: 30 AU Solar system Part 2 Planet Builders nearest: 4.25 ly Stars Part 3 Star Lab 100,000 ly across Galaxies Part 4 Galaxy Mappers light-seconds away billions of light-years away

Four parts, one driving question.

Your team leads one part and teaches it. The class needs all four to plan a mission and to place Earth in the universe.

Start here · How to use these slides

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Part 1 · Moon Watch lead this part

Earth, Moon, and Sun

  • Explain why a bigger telescope sees fainter things.
  • Explain where the Moon and its craters came from.
  • Explain the seasons with tilt, not distance.
  • Name a Moon phase from its angle to the Sun.
  • Explain why eclipses are rare and tides repeat.
The Sun, Earth, and Moon, not to scaleThe Sun, at the left, lights the left half of Earth and the left half of the Moon. A dashed circle shows the Moon's orbit around Earth. Sizes and distances are not to scale. Sun Earth Moon not to scale

Part 1 · Key idea · Tools of astronomy

A telescope's main job is to collect light

Bigger mirrors catch more of the same light The same even rain of light from a faint galaxy falls on two telescope mirrors drawn to scale. Hubble's mirror is 2.4 metres across. Webb's is 6.5 metres across, so its circle has 7.3 times the area and catches 7.3 times as many of the dots. Webb's real mirror is 18 hexagons with gaps, which NASA puts at more than six times Hubble's collecting area. NASA also says Hubble's mirror collects 40,000 times more light than the human eye. an even rain of light from a faint galaxy Hubble · 2.4 m 40,000 × your eye Webb · 6.5 m 7.3 × the area (6.5 ÷ 2.4)² = 7.3 mirrors to scale

A telescope gathers light from far away and brings it to a focus.

A wider lens or mirror catches more light, the way a wider bucket catches more rain. So fainter, farther things show up.

RuleLight caught grows with area, so with diameter squared.

Part 1 · Worked example · Moon Watch's calculation

How much more light, and how much bigger?

A two-lens telescope, drawn to scale Parallel light enters a weak front lens, the objective, with a focal length of 30 centimetres. The rays meet at the focus, then pass through a strong eyepiece with a focal length of 5 centimetres placed 5 centimetres beyond the focus, and leave parallel again toward the eye. The tube is 35 centimetres long. focus objective eyepiece objective focal length · 30 cm 5 cm drawn to scale
Focal length: how far behind a lens parallel light comes to a point. Magnification: how many times wider a far object looks.
Mirrors
Webb 6.5 m · Hubble 2.4 m
Your lenses
objective 30 cm · eyepiece 5 cm
  1. Diameter ratio6.5 m ÷ 2.4 m = 2.71
  2. Area ratio2.71² = 7.3
  3. Magnification30 cm ÷ 5 cm = 6
  4. Read itAs a full disc, Webb's mirror would catch 7.3 times the light. Its real mirror is 18 hexagons with gaps, so NASA says more than 6 times. Your telescope makes the Moon look 6 times wider.
Answer

About 7 times the area as full discs (NASA, for the real mirrors: more than 6); 6× magnification. Check: m ÷ m and cm ÷ cm leave no unit, so both are pure ratios.

Part 1 · Key idea · Tools of astronomy

Air blocks most kinds of light, so some telescopes fly

Which kinds of light reach the ground The electromagnetic spectrum, from long radio waves on the left to short gamma rays on the right. Arrows show how far each kind of light gets through Earth's air. Radio waves and visible light reach the ground, and so do most microwaves. Infrared is mostly absorbed, except through a few windows. Ultraviolet stops in the ozone layer. X-rays and gamma rays are absorbed high up. Telescopes for those kinds of light have to work from space. radiomicrowaveinfraredvisibleUVX-raygamma ← long waves short waves → space ozone layer Earth's air mostly absorbed a few windows absorbed high up: telescopes go to space radio dish your eye heights not to scale

The electromagnetic spectrum is the full range of light, from radio waves to gamma rays.

Earth's air lets visible light and radio waves through. It absorbs most ultraviolet, X-rays, gamma rays, and much infrared.

SoThose telescopes work from space.

Part 1 · Key idea · The Moon

Impacts made the Moon's craters, and almost nothing wears them away

How an impact crater forms, and why the Moon keeps its craters Top: a cross-section of the ground. A rock from space strikes at high speed and blasts out a bowl with a raised rim. Broken rock thrown out of the bowl, called ejecta, lands around it and can streak outward as bright rays. NASA gives Tycho crater as more than 85 kilometres wide. Bottom: on Earth, wind, water, and moving plates erase craters. On the Moon, with almost no air and no liquid water, craters can last billions of years. a rock from space tens of km per second rim bowl ejecta rays Tycho crater: more than 85 km wide Earth wind, water, plates erase them Moon no air or liquid water: they last

An impact crater is a bowl blasted out by a rock from space.

With almost no air or liquid water, the Moon keeps craters for billions of years. On Earth, weather and moving plates erase them.

Crater trayHigher drop, faster hit, wider crater.

Part 1 · Key idea · The Moon

A giant impact probably made the Moon

How the Moon probably formed, in three steps Step 1: about 4.5 billion years ago, a body about the size of Mars hits the young Earth. Step 2: molten and vaporized debris from both bodies spreads into a ring around Earth. Step 3: the debris gathers into a molten Moon, and lighter rock floats up to make its crust. Bottom: iron cores as a share of each body's mass. Earth's core is about 30 percent of its mass. The Moon's core is only about 1.6 to 1.8 percent. 1 · Impact a Mars-sized body hits 2 · Debris ring molten rock rings Earth light crust 3 · Moon forms light rock floats up Iron core as a share of total mass Earth ≈ 30% Moon ≈ 1.6–1.8%

About 4.5 billion years ago, something about the size of Mars probably hit the young Earth. Debris from both bodies gathered into the Moon.

EvidenceApollo rocks, signs of a once-molten surface, and a tiny iron core.

Part 1 · Key idea · The Sun-Earth-Moon system

Tilt, not distance, makes the seasons

Earth's tilted axis at two points in its orbit The Sun sits in the middle of Earth's orbit, drawn in perspective. In early January Earth is at its closest, 147.1 million kilometres from the Sun, yet the north end of its axis leans away from the Sun, so it is northern winter. In early July Earth is at its farthest, 152.1 million kilometres away, and the north end leans toward the Sun, so it is northern summer. The axis points the same way in space all year. the axis points the same way all year Sun N N early January 147.1 million km northern winter early July 152.1 million km northern summer closest in January, yet winter in Houston drawn in perspective: the real orbit is almost a circle

Axial tilt: Earth's spin axis leans 23.4° and keeps pointing the same way all year.

Your half of Earth has summer when it leans toward the Sun. Earth is closest to the Sun in January.

DistanceIt changes sunlight only about 7%, planet-wide.

Part 1 · Key idea · The Sun-Earth-Moon system

A low Sun spreads the same beam over more ground

The same beam of sunlight at noon in June and in December, at 30 degrees north Two panels at Houston's latitude, 30 degrees north. In June the noon Sun stands 83.5 degrees above the horizon and a beam lands on a patch of ground just as wide as the beam. In December the noon Sun is only 36.5 degrees up, and the same beam spreads over 1.7 times as much ground, so each square metre gets less energy. Daylight also runs about 14 hours in June and about 10 hours in December. June noon December noon 83.5° 36.5° covers 1.0 × the beam ≈ 14 h of daylight covers 1.7 × the beam ≈ 10 h of daylight N S N S

Insolation is the sunlight energy that reaches each square metre of ground.

A low winter Sun spreads its beam wide, and short days give the ground fewer hours to warm.

SummerA high Sun and long days, together.

Part 1 · Worked example · Practice Gym skill

How high is the noon Sun over Houston?

The noon Sun's height over Houston through the year A half-dome of sky over an observer at 30 degrees north. Due south, the noon Sun stands 83.5 degrees above the horizon at the June solstice, 60 degrees at the equinoxes, and 36.5 degrees at the December solstice. June and December differ by 47 degrees, twice the 23.5 degree tilt. June · 83.5° equinox · 60° Dec. 36.5° you, at 30° N N S June − December = 47° = 2 × 23.5°
Latitude
L = 30° N (Houston ≈ 29.8° N)
Declination δ
+23.5° June · 0° equinox · −23.5° December
  1. Rulealtitude = 90° − L + δ
  2. June90° − 30° + 23.5° = 83.5°
  3. December90° − 30° − 23.5° = 36.5°
  4. Spread1 ÷ sin 36.5° = 1.68, so December's beam covers 1.68 times as much ground.
Answer

June 83.5°, December 36.5°. Check: they differ by 47°, twice the tilt.

Classroom model: the Practice Gym rule, valid while the noon Sun stays on the equator side of straight overhead. Solar declination (δ) is the latitude where the noon Sun is straight overhead; the Gym rounds the tilt to 23.5° (NASA lists 23.44°, Earth Fact Sheet). Check real dates: NOAA Solar Calculator.

Part 1 · Key idea · The Sun-Earth-Moon system

Half the Moon is always lit. A phase is how much of that half we see

The Moon's phases, seen from above the North Pole Sunlight arrives from the right. Earth is in the middle and the Moon circles it counterclockwise. On the inner ring, the Moon's right half is always lit because it faces the Sun. The outer ring shows what we see from Earth at each spot: new moon when the Moon is between Earth and the Sun, then waxing crescent, first quarter at 90 degrees east of the Sun, waxing gibbous, full moon at 180 degrees, waning gibbous, third quarter at 270 degrees, and waning crescent. Earth's shadow points away from the Sun and plays no part in the phases. sunlight from the Sun Earth New moonWaxing crescentFirst quarterWaxing gibbousFull moonWaning gibbousThird quarterWaning crescent
Inner ring: the Moon seen from above. Outer ring: what you see from Earth. Filled means sunlit.

Sunlight always lights half of the Moon. A phase is how much of that lit half faces Earth.

Elongation: the Moon's angle east of the Sun. New is 0°, first quarter 90°, full 180°.

Not a shadowThe dark part is the Moon's own night side.

Part 1 · Worked example · Practice Gym skill

The Moon is 135° east of the Sun. What phase, and when does it rise?

A Moon 135 degrees east of the Sun, and when each phase rises Left: seen from above, Earth with the Sun's direction to the right and the Moon 135 degrees around its orbit, counterclockwise from the Sun. Right: a ladder of phases every 45 degrees with their approximate rise times. New moon rises near 6 a.m., waxing crescent near 9 a.m., first quarter near noon, waxing gibbous near 3 p.m., and full moon near 6 p.m. The 135 degree row, waxing gibbous, is highlighted. to the Sun 135° Moon Earth from above the North Pole 0°New · rises ≈ 6 a.m.45°Waxing crescent · ≈ 9 a.m.90°First quarter · ≈ noon135°Waxing gibbous · ≈ 3 p.m.180°Full · ≈ 6 p.m.
Elongation
θ = 135° east of the Sun
Model
each 45° = the next phase; 15° ≈ 1 hour of rise time
  1. Count135° ÷ 45° = 3 phases past new
  2. Name itnew → waxing crescent → first quarter → waxing gibbous
  3. Delay135° ÷ 15° per hour = 9 hours after the Sun
  4. Clocksunrise ≈ 6 a.m. + 9 h ≈ 3 p.m.
Answer

Waxing gibbous, rising mid-afternoon. Check: it falls between first quarter (noon) and full (sunset).

Classroom model: the Practice Gym's phase table. Real rise times also shift with season and latitude. Full Moon rises near sunset, third quarter near midnight: NASA Moon Phases. The Moon rises about 50 minutes later each day: NOAA, the lunar day.

Part 1 · Worked example · Moon Watch's calculation

How long is a Moon-base night, and what does it cost?

Why the phase cycle is longer than one orbit Seen from above, the Sun is on the left and Earth moves up along its orbit. On day 0 the Moon sits between Earth and the Sun: new moon. After 27.32 days the Moon has gone once around Earth compared with the distant stars, but Earth has moved about 27 degrees along its orbit, so the Moon is not yet lined up with the Sun. It lines up again, new moon, on day 29.53, about 2.2 days later. Sun Day 0 new moon Day 27.32 1 orbit vs. the stars Day 29.53 new again (dashed) same star direction Earth moves ≈ 27° from above · not to scale
Synodic month: one full cycle of phases, new moon to new moon.
Orbits
Moon 27.32 d (vs. the stars) · Earth 365.25 d
Base power
40 kW, day and night
  1. Rates per day1 ÷ 27.32 = 0.036603; 1 ÷ 365.25 = 0.002738
  2. Subtract0.036603 − 0.002738 = 0.033865
  3. Phase cycle1 ÷ 0.033865 = 29.53 days
  4. One night29.53 ÷ 2 = 14.77 days = 354 h
  5. Energy354 h × 40 kW ≈ 14,200 kWh
Answer

About 14.8 days of dark and 14,200 kWh per night. Check: 29.53 days matches NASA.

Part 1 · Key idea · The Sun-Earth-Moon system

Eclipses are rare because the Moon's orbit is tipped about 5°

Edge-on view of the Moon's tilted orbit and Earth's shadow Two edge-on views with the Sun on the left and Earth's shadow stretching to the right. Top: most months the full Moon passes above or below the shadow because the Moon's orbit is tilted about 5 degrees, drawn steeper here. Bottom: in an eclipse season the full Moon crosses the line where its orbit meets Earth's orbital plane, so it enters the shadow and there is a lunar eclipse. Most months: the full Moon misses the shadow full Moon Earth's shadow Moon's orbit (tilt drawn steeper than 5.1°) Eclipse season: the full Moon enters the shadow lunar eclipse At new moon: the Moon's shadow on Earth, a solar eclipse.

A lunar eclipse: the full Moon passes through Earth's shadow.

A solar eclipse: the new Moon's shadow falls on Earth.

Most months the Moon passes above or below the shadow, so eclipses come only in a few short seasons each year.

Part 1 · Key idea · The Sun-Earth-Moon system

The Moon stretches the ocean into two bulges

How the Moon's uneven pull makes two tidal bulges Top: Earth with its ocean stretched into two bulges, one toward the Moon and one on the far side, greatly exaggerated. Middle: the Moon pulls the near side hardest, Earth's centre less, and the far side least, so Earth is stretched both ways. Bottom: when the Sun, Earth, and Moon line up at new and full moon, the pulls add and make spring tides with the biggest range. When they are at right angles at the quarter moons, they partly cancel and make neap tides. Earth Moon bulge toward the Moon bulge on the far side bulges hugely exaggerated far: least centre near: most pull toward the Moon lined up: spring tide new and full moon right angle: neap tide quarter moons
Spring tides have the biggest range; neap tides the smallest. Each comes twice a month.

A tide is the regular rise and fall of sea level.

The Moon pulls the near side hardest and the far side least, stretching the ocean into two bulges. Earth spins through both.

GalvestonNOAA: the Gulf often gets one high tide a day.

Part 1 · Common mistakes

Three Earth–Moon mistakes that cost points

Earth is closest to the Sun in January, during northern winter January: closest July
✗ Mistake

“Summer comes when Earth is closest to the Sun.”

✓ Fix

Earth is closest in early January, during northern winter. Tilt makes the seasons.

At first quarter, Earth's shadow points away from the Moon shadow sunlight
✗ Mistake

“A crescent is Earth's shadow on the Moon.”

✓ Fix

The dark part is the Moon's own night side. Earth's shadow reaches it only in a lunar eclipse.

Twelve full moons a year, but eclipses only in two seasons full moons in a year · red = eclipse
✗ Mistake

“There is a lunar eclipse every full moon.”

✓ Fix

The 5° tilt makes the Moon miss the shadow most months, so eclipses come in seasons.

Part 1 · Check yourself

Two quick checks

At 40° N on the December solstice, how high is the noon Sun? (Use δ = −23.5°.)

Show the answer

A, 26.5°. 90° − 40° + (−23.5°) = 26.5°. B leaves out δ (that is the equinox). C adds 23.5° (that is June). D adds 23.5° to the latitude instead of using the rule.

The Moon sits 270° east of the Sun. Which phase do you see?

Show the answer

C, third quarter. 270° ÷ 45° = 6 steps past new: crescent, first quarter, gibbous, full, gibbous, third quarter. It rises near midnight. A is 90°, B is 180°, D is 315°.

Part 2 · Planet Builders lead this part

How the solar system was built

  • Explain how a spinning cloud became the Sun and planets.
  • Explain why inner planets are rocky and outer ones giant.
  • Use density to tell what a world is made of.
  • Find a planet's year from its distance.
  • Tell asteroids, comets, and meteoroids apart.
Rocky planets near the Sun, giants beyond the frost lineThe Sun at the left with orbits around it. Three small rocky planets orbit inside a dashed frost line; two large gas giants and a smaller icy giant orbit beyond it. frost line rocky giants

Part 2 · Key idea · Formation of the solar system

A spinning cloud flattened into a disk and built the planets

From a cloud to a disk to planets Three panels. Step 1: about 4.6 billion years ago a cloud of gas and dust collapses under its own gravity. Step 2: as it shrinks it spins faster and flattens into a disk, with the young Sun forming in the middle. The Sun ends up with 99.8 percent of the mass. Step 3: in the disk, dust grains stick together into clumps called planetesimals, which collide and grow into planets. 1 · Cloud collapses gravity pulls it in spins faster 2 · Spinning disk Sun forms in the middle 3 · Grains stick clumps grow into planets about 4.6 billion years ago · the Sun kept 99.8% of the mass

The solar nebula was a spinning cloud of gas and dust. It collapsed into a disk with the Sun at the centre.

In the disk, grains stuck together: accretion. Clumps grew into planetesimals, small rocky or icy bodies, then into planets.

Part 2 · Key idea · Inner and outer planets

Past the frost line, ice helped build giant planets

The eight planets, sizes to scale, distances on a log scale The Sun is at the left. Planet sizes are drawn to scale with each other, and distance from the Sun runs along a log scale. Mercury at 0.39 AU, Venus at 0.72, Earth at 1.00, and Mars at 1.52 are tiny rocky worlds inside the frost line, where only rock and metal stayed solid. Beyond the frost line, between Mars and Jupiter, ice also stayed solid. Jupiter at 5.20 AU and Saturn at 9.57 are gas giants. Uranus at 19.16 and Neptune at 30.18 are ice giants. frost linetoo warm for ice:rock and metal onlyice stays solid too:more to build withMercury0.39 AUVenus0.72 AUEarth1.00 AUMars1.52 AUJupiter5.20 AUSaturn9.57 AUUranus19.16 AUNeptune30.18 AU sizes to scale · distance on a log scale
Terrestrial planets: Mercury, Venus, Earth, Mars. Gas giants: Jupiter and Saturn; Uranus and Neptune are ice giants.

Near the young Sun only rock and metal stayed solid, so the inner planets are small and rocky.

Past the frost line, ice stayed solid too. Bigger cores grew there and pulled in gas.

Orbit tableMark the frost line between Mars and Jupiter.

Part 2 · Key idea · Inner and outer planets

Density tells you what a world is made of

Mean density of each planet and the Moon Bar chart of mean density in grams per cubic centimetre. Mercury 5.43, Venus 5.24, Earth 5.51, the Moon 3.34, Mars 3.93, Jupiter 1.33, Saturn 0.69, Uranus 1.27, Neptune 1.64. Dashed lines mark surface rock at about 2.7 and water at 1.0. The rocky worlds sit well above surface rock because they hold dense iron cores. The giants sit near water, because they are mostly hydrogen, helium, and ices. 0123456density (g/cm³)5.43Mercury5.24Venus5.51Earth3.34Moon3.93Mars1.33Jupiter0.69Saturn1.27Uranus1.64Neptunesurface rock ≈ 2.7water 1.0rocky worlds: iron coresgiants: gas and ice

Density is mass ÷ volume.

Earth averages 5.51 g/cm³ but its surface rock only about 2.7, so something denser, an iron core, hides inside.

DifferentiationIn a molten world, heavy metal sinks and light rock floats up into layers.

Part 2 · Key idea · Inner and outer planets

Farther planets move slower and take longer to go around

Orbit time against distance for the eight planets A log-log plot of each planet's orbit time in Earth years against its average distance from the Sun in astronomical units. Mercury 0.39 AU and 0.24 years, Venus 0.72 and 0.62, Earth 1 and 1, Mars 1.52 and 1.88, Jupiter 5.20 and 11.86, Saturn 9.57 and 29.42, Uranus 19.16 and 83.75, Neptune 30.18 and 163.7. All eight fall on one straight line, P squared equals a cubed. 1 AU10 AU1 yr10 yr100 yrP² = a³MercuryVenusEarthMarsJupiterSaturnUranusNeptuneaverage distance from the Sun, a (log scale)orbit time, P (log scale)

An astronomical unit (AU) is Earth's average distance from the Sun, 149.6 million km.

Kepler's third law: P² = a³, with P in Earth years and a in AU.

Read itEach gridline is 10 times the last.

Part 2 · Worked example · Planet Builders' calculation

How long is a year on Mars, and on Jupiter?

How far each planet gets in one Earth year Orbits of Earth, Mars, and Jupiter drawn to scale around the Sun. All three start on the right. In one Earth year, Earth makes one full lap, Mars covers about 53 percent of its orbit, and Jupiter only about 8 percent. start Earth Mars Jupiter In 1 Earth year: Earth 1 lap · Mars 53% · Jupiter 8% to scale
Mars
a = 1.524 AU
Jupiter
a = 5.20 AU
Earth year
365.25 days
  1. Cube1.524³ = 3.540
  2. Square root√3.540 = 1.881 years
  3. Days1.881 × 365.25 = 687.2 days
  4. Jupiter5.20³ = 140.6; √140.6 = 11.86 years
Answer

Mars: 1.881 years (687 days). Jupiter: 11.86 years. Check: NASA lists 686.98 days for Mars.

Part 2 · Key idea · Other objects in the solar system

Asteroids and comets are leftover building blocks

The asteroid belt and a comet's path Seen from above, the Sun is on the left. Most asteroids orbit in the main belt between the orbits of Mars and Jupiter. A comet follows a long, stretched orbit. Near the Sun its ice turns to gas and dust, and its tail points away from the Sun. Far from the Sun it is a frozen nucleus with no tail. Mars Jupiter main asteroid belt comet near the Sun: tail points away from the Sun far out: frozen, no tail from above · not to scale

An asteroid is a rocky leftover; most orbit between Mars and Jupiter.

A comet is an icy leftover. Near the Sun it heats up and grows a tail.

A meteoroid is a smaller rock in space. Burning up in air, it makes a meteor.

Part 2 · Key idea · Inner and outer planets

Every planet's tilt sets its own seasons

How far each planet's spin axis tilts Eight planets in a row, each with its spin axis drawn at its tilt from straight up. Mercury 0.03 degrees, Venus 177.4 degrees (spinning upside down), Earth 23.4, Mars 25.2, Jupiter 3.1, Saturn 26.7, Uranus 97.8 (lying on its side), Neptune 28.3. The dot marks each planet's north pole. Mercury0.03°Venus177.4°Earth23.4°Mars25.2°Jupiter3.1°Saturn26.7°Uranus97.8°Neptune28.3° sizes not to scale · dot = north pole

Mars leans 25.2°, close to Earth's 23.4°, so it has seasons too. Its year is 687 days, so each season lasts about twice as long.

Uranus lies on its side: each pole gets decades of sunlight, then decades of dark.

Part 2 · Common mistakes

Three solar system mistakes to avoid

The Sun and Earth at true scale: Earth is a speck 107 Sun-widths away Sun Earth true scale: Earth is too small to see
✗ Mistake

“Solar system pictures show the real sizes and gaps.”

✓ Fix

Earth is 109 times narrower than the Sun and 107 Sun-widths away. Most pictures are not to scale.

Orbital speed falls with distance: Jupiter 13.1 km/s, Pluto 4.7 km/s Jupiter Pluto 13.1 4.7 km/s
✗ Mistake

“Outer planets are slow because they are big.”

✓ Fix

Speed depends on distance from the Sun, not size. Tiny Pluto is slower than huge Jupiter.

A comet leaving the Sun still has its tail pointing away from the Sun heading out, tail in front
✗ Mistake

“A comet's tail streams out behind it.”

✓ Fix

The tail points away from the Sun, whichever way the comet is moving.

Part 2 · Check yourself

Two quick checks

A planet orbits the Sun at 4 AU. How long is its year?

Show the answer

B, 8 years. P² = 4³ = 64, so P = √64 = 8. A is √4; C is 4²; D stops at a³ and forgets the square root.

A newly found planet has a density of 1.3 g/cm³. What is it mostly made of?

Show the answer

C. 1.3 g/cm³ is close to Jupiter's 1.33 and near water's 1.0. Rock alone is about 2.7 or more (B, D); iron-rich worlds are above 5 (A).

Part 3 · Star Lab lead this part

Stars: how they shine, and how they end

  • Explain what powers the Sun.
  • Measure the Sun's width with a pinhole.
  • Compare stars by distance, size, and heat.
  • Read an H-R diagram.
  • Predict a star's life from its mass.
Stars of different colours and sizesFour stars compared, not to scale: a huge red giant, a hot blue star larger than the Sun, the Sun, and a tiny white dwarf. Sun red giant hot blue star white dwarf

Part 3 · Key idea · The Sun

The Sun shines by fusing hydrogen into helium

Inside the Sun A cutaway of the Sun. In the core, at about 15 million degrees Celsius, hydrogen nuclei fuse into helium and release energy. The energy travels out through the radiative zone, then rises and sinks in the convection zone, and leaves from the visible surface, the photosphere, at 5,772 K. A strip below shows four hydrogen nuclei becoming one helium nucleus plus energy. core≈ 15 million °C radiative zone convection zone photosphere5,772 K surface HHHH He + energy fusion in the core: 4 hydrogen nuclei → 1 helium

The Sun is a star: a ball of hot hydrogen and helium held together by its own gravity.

In its core, nuclear fusion joins hydrogen nuclei into helium and releases energy.

Every secondThe Sun turns about 4 million tonnes of mass into energy.

Part 3 · Worked example · Star Lab's calculation

How wide is the Sun? Measure it with a pinhole

Same-shape triangles through a pinhole Light from the top and bottom edges of the Sun crosses at a pinhole and makes an upside-down image on a screen 1,000 millimetres behind it. The image is 9.3 millimetres wide. The big triangle from the Sun to the pinhole and the small triangle from the pinhole to the screen have the same shape, so the Sun's width divided by 150 million kilometres equals 9.3 millimetres divided by 1,000 millimetres. Not to scale. pinhole card screen 9.3 mm 150,000,000 km 1,000 mm Sun: width D
Never look at the Sun, even through the pinhole. Look only at the image on the paper, with your back to the Sun.
Image width
9.3 mm
Screen distance
1,000 mm
Sun's distance
150,000,000 km
  1. Ratio9.3 mm ÷ 1,000 mm = 0.0093
  2. Same shapeD ÷ 150,000,000 km = 0.0093
  3. MultiplyD = 0.0093 × 150,000,000 km = 1,395,000 km
Answer

About 1.4 million km. Check: NASA gives 1.39 million km, within 0.3%.

Part 3 · Key idea · Measuring the stars

Twice as far looks one-fourth as bright

The same light spread over more area Light leaves a point source and spreads out. At distance d it covers one square. At twice the distance it covers four squares of the same size, so each square gets one-fourth as much. At three times the distance it covers nine squares, one-ninth each. 1 ¼ 1/9 distance d 1 square 2d 4 squares, ¼ each 3d 9 squares, 1/9 each star brightness falls as 1 ÷ distance²

Luminosity is the total light a star gives off. Apparent brightness is how bright it looks from here.

Light spreads over a sphere's area, 4πd², so brightness falls as 1 ÷ d².

Starlight benchDouble the distance; the lux reading drops to about ¼.

Part 3 · Worked example · Practice Gym skill

Same star, three times farther: how bright does it look?

Two identical stars at distances d and 3d Two stars with the same luminosity. Star A is at distance d and star B is three times as far. A bar chart of apparent brightness shows A at 1 and B at one-ninth. you A at d B at 3d how bright each one looks A B 1 1/9
Stars
same luminosity
Distances
B is 3 times as far as A
  1. Rulebrightness falls as 1 ÷ d²
  2. Square3² = 9
  3. CompareB looks 1/9 as bright; A looks 9 times brighter
  4. ReverseIf B looked 1/25 as bright: √25 = 5 times as far
Answer

B shows 1/9 of A's brightness. Check: farther must look dimmer, and 1/9 is less than 1.

Part 3 · Key idea · Measuring the stars

A star's colour gives away its surface temperature

Star colour against surface temperature A temperature scale running from 40,000 kelvin on the left to 2,500 kelvin on the right, coloured from blue through white and yellow to orange and red. Spica at 22,400 K and Rigel at 12,100 K are blue-white. Sirius A at 9,940 K is white. The Sun at 5,772 K is yellow-white. Betelgeuse at about 3,500 K is orange-red. Proxima Centauri at 3,042 K is a cool red dwarf. 40,000 K10,000 K5,000 K2,500 KSpica22,400 KRigel12,100 KSirius A9,940 KSun5,772 KBetelgeuse3,500 KProxima3,042 K← hotter, bluercooler, redder →

Hot things glow bluer; cooler things glow redder. Stars follow the same rule.

Temperatures are in kelvin (K): degrees Celsius plus 273.

Star-fate wheelGive each mass its colour.

Part 3 · Key idea · Measuring the stars

The H-R diagram sorts stars by temperature and luminosity

An H-R diagram with nine real stars Surface temperature runs from 40,000 kelvin on the left to 2,500 kelvin on the right. Luminosity runs from one ten-thousandth of the Sun at the bottom to a million Suns at the top, each gridline a hundred times the last. A diagonal band, the main sequence, holds the Sun (5,772 K, 1), Sirius A (9,940 K, 25), Spica (22,400 K, 20,500) and Proxima Centauri (3,042 K, 0.0017). Upper right: the red giant Aldebaran (3,900 K, 439) and the supergiants Betelgeuse (3,500 K, about 126,000) and Rigel (12,100 K, about 120,000). Lower left: white dwarfs Sirius B (25,000 K, 0.026) and Procyon B (7,740 K, 0.00049). Dashed lines mark stars 100, 1, and 0.01 times the Sun's radius. 0.00010.01110010,0001,000,00040,000 K10,0005,0002,500 K100 × Sun's radiusSun's radius0.01 × Sun's radiusmain sequencered giantswhite dwarfssupergiantsSunSirius ASirius BRigelBetelgeuseProxima CentauriSpicaAldebaranProcyon Bsurface temperature (hot on the left, log scale)luminosity, Sun = 1 (log scale)

An H-R diagram plots temperature (hot on the left) against luminosity.

About 90% of stars sit on the main sequence: stars fusing hydrogen in their cores. Each star stays at one spot there.

Read itOff the band: cool giants are huge; hot white dwarfs are tiny.

Part 3 · Worked example · Practice Gym skill

Half as hot but 100 times wider: how luminous?

Size and temperature both vote on luminosity The Sun is drawn as a small dot. A star 100 times wider is drawn at the same scale as a huge arc. Its surface area is 100 squared, 10,000 times the Sun's, which raises luminosity. Its temperature is half the Sun's, and half to the fourth power is one-sixteenth, which lowers it. Together: 10,000 times one-sixteenth equals 625 times the Sun's luminosity. Sun 100 × wider, half as hot area vote: × 10,000 100² = 10,000 heat vote: × 1/16 0.5⁴ = 0.0625 result: × 625 a red giant sizes to scale
Temperature
T = 0.5 × the Sun's
Radius
R = 100 × the Sun's
  1. RuleL ÷ LSun = (R ÷ RSun)² × (T ÷ TSun)⁴
  2. Area vote100² = 10,000
  3. Heat vote0.5⁴ = 0.0625
  4. Multiply10,000 × 0.0625 = 625
Answer

625 times the Sun's luminosity: a red giant. Check: cooler alone would mean dimmer, but size wins here.

Practice Gym skill: the ratio form of the Stefan–Boltzmann law, L = 4πR²σT⁴; the constants 4π and σ cancel (NIST, σ).

Part 3 · Key idea · Stellar evolution

A star's mass at birth decides how it lives and dies

Four life paths, set by a star's mass at birth Four rows, one per mass band, using the Practice Gym's classroom bands. Under 0.5 Suns: a red dwarf fuses hydrogen for far longer than the universe's current age, then cools into a white dwarf with no giant stage. From 0.5 to 8 Suns, like the Sun: a red giant, then a planetary nebula, leaving a white dwarf. From 8 to 20 Suns: a red supergiant, then a supernova, leaving a neutron star. Over 20 Suns: a supergiant, then a supernova, leaving a black hole. main sequencegiant stagethe endwhat is leftunder 0.5Suns0.5 to 8Suns8 to 20Sunsover 20Sunsfuses longer than the universe has existedno giant stagewhite dwarfthe Sunred giantplanetary nebulawhite dwarfsupergiantsupernovaneutron starsupergiantsupernovablack hole
Red giant: swollen, cool, bright. Planetary nebula: its shed gas. White dwarf: the Earth-sized core left. Supernova: a massive star's blast, leaving a neutron star or black hole.

Mass sets a star's temperature, brightness, lifetime, and ending.

Heavier stars burn hotter and die sooner.

ModelCut-offs are the Practice Gym's classroom bands, also used in the lab. Real boundaries blur.

Under 8 Suns: red giant, then white dwarf; 8 to 20 Suns: neutron star; heavier: black hole: NASA Star Types. The 0.5-Sun band and its "no giant stage" rule are the Practice Gym and Orbit & Starlight models.

Part 3 · Worked example · Star Lab's calculation

How long does a 2-Sun star last? A 15-Sun star?

Main-sequence lifetime by mass, from the classroom rule A bar chart on a log scale of years. From the rule lifetime equals 10 billion years divided by mass to the 2.5 power: 1 Sun, 10 billion years; 2 Suns, 1.77 billion years; 5 Suns, 179 million years; 15 Suns, 11.5 million years. A dashed line marks the age of the universe, 13.8 billion years. age of the universe, 13.8 billion yr 1 Sun10 billion yr 2 Suns1.77 billion yr 5 Suns179 million yr 15 Suns11.5 million yr 1 million10 million100 million1 billion10 billion years on the main sequence (log scale)
Rule
lifetime = 10 billion yr ÷ M2.5
M
mass in Suns: 2 and 15
  1. Power22.5 = 5.66
  2. Divide10 ÷ 5.66 = 1.77 billion years
  3. 15 Suns152.5 = 871; 10 ÷ 871 = 0.0115 billion years
  4. Convert0.0115 × 1,000 million = 11.5 million years
Answer

2 Suns: 1.77 billion years. 15 Suns: 11.5 million years, then a supernova. Check: 1.77 × 5.66 = 10.0.

Classroom rule of thumb used by the Practice Gym and the Orbit & Starlight lab; the lab notes it holds to about a factor of two between 0.4 and 20 Suns. The Sun: 4.6 billion years old, about 5 billion more on the main sequence: NASA Star Types.

Part 3 · Key idea · Stellar evolution

Stars made the atoms in Earth and in you

Where the elements come from A cycle of four boxes. 1: in the first minutes after the Big Bang, hydrogen and helium formed. 2: stars fuse those into heavier elements such as carbon, oxygen, and calcium, up to iron. 3: supernova explosions forge many elements heavier than iron, including gold, iodine, and most natural radioactive elements such as uranium, and scatter them into space. 4: that enriched gas and dust forms new stars and planets, including the Sun, Earth, and the calcium in your bones and iron in your blood. The cycle repeats. new stars 1 · Big Bang 2 · Stars fuse 3 · Supernovas 4 · New worlds first few minutes up to iron, then stop heavier than iron Sun, Earth, and you HHe COCaFe AuUI fusing iron gives no energy gold, uranium, iodine calcium in bones, iron in blood

The first minutes made hydrogen and helium. Stars fuse them into heavier elements, up to iron.

Supernovas forge many elements heavier than iron, such as gold and uranium, and scatter them. New stars and planets form from that dust.

Part 3 · Common mistakes

Three star mistakes to avoid

Cool and huge outshines hot and tiny cool,huge hot, tiny
✗ Mistake

“The brightest stars must be the hottest.”

✓ Fix

Betelgeuse is cooler than the Sun but so huge it gives off about 126,000 times the Sun's light.

A star stays at one spot on the main sequence no sliding along the band
✗ Mistake

“Stars slide down the main sequence as they age.”

✓ Fix

Residence, not route: a star stays put while it fuses hydrogen, then leaves the band.

The Sun's path: red giant, then white dwarf Sun red giant white dwarf
✗ Mistake

“The Sun will explode as a supernova.”

✓ Fix

With under 8 Suns of mass, it will become a red giant, then a white dwarf.

Part 3 · Check yourself

Three quick checks

A star is twice the Sun's temperature and half its radius. How many times the Sun's luminosity is it?

Show the answer

B, 4. 0.5² × 2⁴ = 0.25 × 16 = 4. A multiplies 2 × 0.5 with no powers; C forgets to square the radius; D leaves the radius out.

A star forms with 25 Suns of mass. In the Practice Gym model, how does it end?

Show the answer

D. Over 20 Suns the collapsed core becomes a black hole. C is the 8–20 band, B is 0.5–8, A is under 0.5.

Star B looks 1/16 as bright as an identical star A. How many times farther is B?

Show the answer

A, 4. Brightness falls as 1 ÷ d², so d = √16 = 4. B halves 16; C ignores the square; D squares instead of taking the root.

Part 4 · Galaxy Mappers lead this part

Galaxies and the expanding universe

  • Use light-years, and explain why far means long ago.
  • Find the Sun in the Milky Way.
  • Sort galaxies by shape.
  • Use Hubble's law to find a speed or a distance.
  • Give the evidence for the Big Bang.
A spiral galaxy and distant galaxiesA spiral galaxy with two curving arms around a bright central bulge, and three small, faint galaxies far away in the background.

Part 4 · Key idea · The Milky Way

A light-year is a distance, and looking far means looking back

Distances in light-years, on a log scale A log scale of distance in light-years. Sunlight takes 8.3 minutes to reach Earth. Proxima Centauri, the nearest star, is 4.25 light-years away, so we see it as it was 4.25 years ago. The Milky Way is about 100,000 light-years across. The Andromeda galaxy is 2.5 million light-years away, so we see it as it was 2.5 million years ago. One light-year is about 9.46 trillion kilometres. 0.00010.01110010,0001 million distance in light-years (log scale) Sun 8.3 light-minutes Proxima Centauri 4.25 ly: seen as it was 4.25 years ago Milky Way, across 100,000 ly Andromeda galaxy 2.5 million ly: seen as it was 2.5 million years ago 1 ly = 299,792 km/s × 31,557,600 s ≈ 9.46 trillion km

A light-year is the distance light travels in one year: about 9.46 trillion km.

Light takes time to arrive. The farther you look, the further back in time you see.

Part 4 · Key idea · The Milky Way

We live inside the disk of a barred spiral galaxy

The Milky Way from above and from the side Left: the Milky Way seen from above, a barred spiral about 100,000 light-years across, with the Sun about 26,000 light-years from the centre, between two arms. Right: the same galaxy seen edge-on, a thin disk with a bulge in the middle. From the Sun, looking along the disk shows a crowded band of stars: the Milky Way across our night sky. The Sun takes about 230 million years to circle the centre. Sun 26,000 ly about 100,000 light-years FROM ABOVE EDGE-ON Sun look along the disk: the band in our sky More than 100 billion stars One lap of the centre about 230 million years

A galaxy is a huge group of stars, gas, and dust held together by gravity.

The Milky Way is about 100,000 light-years across. The Sun orbits about 26,000 light-years from the centre.

Galaxy diskScale 1 cm = 5,000 ly puts the Sun 5.2 cm out.

Part 4 · Key idea · Other galaxies

Galaxies come in three main shapes

Spiral, elliptical, and irregular galaxies Three drawings. A spiral galaxy: a flat disk with curved arms, like the Milky Way and Andromeda, both barred spirals. An elliptical galaxy: a smooth oval of mostly older stars with little gas, like NGC 2865, 100 million light-years away. An irregular galaxy: no clear shape, like the dwarf galaxy NGC 5264. Spiral flat disk with arms Milky Way, Andromeda Elliptical smooth oval, older stars NGC 2865 Irregular no clear shape NGC 5264

Spiral galaxy: a flat, spinning disk with curved arms.

Elliptical galaxy: a smooth oval of mostly older stars and little gas.

Irregular galaxy: no clear shape, often rich in gas.

Galaxy sorterAsk yes-or-no: arms? smooth oval?

Part 4 · Key idea · Other galaxies

Light from far galaxies arrives stretched toward red

Spectral lines shift toward longer wavelengths Top: two spectra from short, blue wavelengths on the left to long, red wavelengths on the right. The same three dark lines appear in both. In the far galaxy's light they sit farther to the right, at longer wavelengths: a redshift. Bottom: a light wave as it left the galaxy, and the same wave arriving here, stretched to one and a half times its wavelength. nearby galaxy far galaxy: same lines, shifted ← shorter, bluer longer, redder → as it left arriving wavelength 2 units stretched to 3 units

Redshift: light's waves arrive stretched to longer, redder wavelengths. We spot it by the shift of known dark lines.

In 1929 Hubble found that farther galaxies show bigger redshifts.

Redshift stretcherStretch 1.5×: 2 cm crests become 3 cm.

Part 4 · Key idea · Cosmology

The farther the galaxy, the faster it moves away

Hubble's law: speed against distance A graph of how fast galaxies move away against their distance in megaparsecs, from 0 to 400. The Practice Gym line, v equals 70 times d, rises straight from the origin to 28,000 kilometres per second at 400 megaparsecs. A shaded wedge shows the range of measured expansion rates, 67 to 74 kilometres per second per megaparsec. Two worked points sit on the line: 120 megaparsecs at 8,400 kilometres per second, and 200 megaparsecs at 14,000. 0100200300400 010,00020,00030,000 distance, d (Mpc) speed away, v (km/s) 120 Mpc · 8,400 km/s 200 Mpc · 14,000 km/s v = 70 × d (Practice Gym) measured: 67 to 74

Hubble's law: v = H₀ × d. A galaxy's speed away grows in step with its distance.

A megaparsec (Mpc) is 3.26 million light-years. The Practice Gym uses H₀ = 70 km/s per Mpc.

Measured H₀ of 74 against 67 from the early universe, and "every 3.3 million light-years": NASA Hubble. 1 parsec = 3.26 ly: NASA Imagine. The Gym's 70 is a classroom value between them.

Part 4 · Worked example · Practice Gym and Galaxy Mappers

Hubble's law both ways: speed from distance, distance from speed

Two galaxies and their speeds away from us The Milky Way at the left. Galaxy A is 120 megaparsecs away and moves away at 8,400 kilometres per second. Galaxy B is 200 megaparsecs away and moves away at 14,000 kilometres per second. Distances and arrow lengths are drawn to scale: the scale bars show 50 megaparsecs and 5,000 kilometres per second. us A · 120 Mpc B · 200 Mpc 8,400 km/s 14,000 km/s 50 Mpc 5,000 km/s to scale
H₀
70 km/s per Mpc (Practice Gym)
Galaxy A
d = 120 Mpc
Galaxy B
v = 14,000 km/s
  1. Speed of Av = 70 × 120 = 8,400 km/s
  2. Rearranged = v ÷ H₀
  3. Distance of Bd = 14,000 ÷ 70 = 200 Mpc
  4. Light-years200 × 3.26 million ≈ 652 million ly
Answer

A: 8,400 km/s. B: 200 Mpc, about 650 million light-years. Check: 8,400 ÷ 120 = 70.

Practice Gym skill: Hubble's law, both directions, H₀ = 70 km/s per Mpc. The same numbers are in the Galaxy Mappers calculation in the team project.

Part 4 · Key idea · Cosmology

Space itself is stretching, so there is no centre

Dots on a balloon before and after it grows Left: a small balloon with a home dot, dot A 3 centimetres away and dot B 6 centimetres away. Right: the same balloon blown up to twice the size. Every distance doubled: A is now 6 centimetres away and B is 12. B moved twice as far as A in the same time. Any dot could be called home and would see the same thing. earlier A B home A: 3 cm · B: 6 cm 10 s 10 s later: twice the size A B home A: 6 cm · B: 12 cm

Galaxies are not flying out from one spot. The space between them is stretching.

From any galaxy, the others move away, and the farther ones move faster.

Model limitBalloon dots sit on a 2-D skin, and the dots stretch. Real galaxies do not stretch.

Part 4 · Worked example · Galaxy Mappers' calculation

Balloon universe: why do farther dots move faster?

Two dots measured from home, before and after Distances measured from the home dot along the balloon. At the start, dot A is 3.0 centimetres away and dot B is 6.0 centimetres away. After 10 seconds, A is 6.0 centimetres away and B is 12.0. A moved 3.0 centimetres and B moved 6.0 centimetres in the same time. start 10 s later homeA · 3.0 cmB · 6.0 cmhomeA · 6.0 cmB · 12.0 cm A moved 3.0 cm B moved 6.0 cm distances measured along the balloon
Dot A
3.0 cm → 6.0 cm from home
Dot B
6.0 cm → 12.0 cm from home
Time
10 s
  1. A's speed(6.0 − 3.0) cm ÷ 10 s = 0.30 cm/s
  2. B's speed(12.0 − 6.0) cm ÷ 10 s = 0.60 cm/s
  3. Speed ÷ start distance0.30 ÷ 3.0 = 0.10 per s; 0.60 ÷ 6.0 = 0.10 per s
Answer

Twice as far, twice as fast. Both dots share one rate, 0.10 per second: the balloon's own Hubble constant.

Part 4 · Key idea · Cosmology

Three lines of evidence point to a hot, dense beginning

A 13.8-billion-year timeline and three lines of evidence Top: a timeline from the Big Bang, 13.8 billion years ago, to today. In the first few minutes hydrogen and helium formed. At 380,000 years the universe became transparent, and that light is the cosmic microwave background. The first stars shone about 200 million years after the start. The Sun and Earth formed 4.6 billion years ago. Bottom: three lines of evidence. One, galaxies move apart, and farther ones faster. Two, a faint microwave glow at 2.725 kelvin arrives from every direction. Three, the amounts of hydrogen and helium match what the first minutes would make. Big Bang · 13.8 billion years ago today Sun and Earth: 4.6 billion years ago first minutes: hydrogen and helium 380,000 years: light set free (the CMB) ≈ 200 million years: first stars 1 · Expansion galaxies move apart; farther ones faster 2 · Microwave glow 2.725 K, from every direction in the sky HHe 3 · Light elements H and He amounts fit the first minutes

The Big Bang theory: the universe has expanded from a hot, dense state for about 13.8 billion years.

The cosmic microwave background is the oldest light we can see, now at 2.7 K.

Law vs. theoryHubble's law describes a pattern. The Big Bang theory explains it.

Part 4 · Common mistakes

Three universe mistakes to avoid

Not an explosion from a centre: the whole grid stretches from one spot space stretches
✗ Mistake

“The Big Bang was an explosion from one centre into empty space.”

✓ Fix

Space itself expanded everywhere at once. There is no centre and no edge to fly toward.

A light-year is a length on a ruler, not a time 1 ly ≈ 9.46 trillion km
✗ Mistake

“A light-year is a length of time.”

✓ Fix

It is a distance: how far light goes in a year, about 9.46 trillion km.

Redshift moves the dark lines, not the galaxy's colour same lines, shifted to longer waves
✗ Mistake

“A redshifted galaxy looks red.”

✓ Fix

Redshift is measured by known dark lines sitting at longer wavelengths than in a lab.

Part 4 · Check yourself

Three quick checks

With H₀ = 70 km/s per Mpc, how fast does a galaxy 300 Mpc away move away from us?

Show the answer

C. v = 70 × 300 = 21,000 km/s. A divides 300 by 70; B subtracts; D adds.

On the balloon universe, which dot is the centre of the expansion?

Show the answer

D. Every dot sees all the others move away, farther ones faster. A only looks special because we measured from it; the knot (B) is not on the surface the dots live on; speed (C) depends on who measures.

Which observation is evidence for the Big Bang?

Show the answer

B. The cosmic microwave background is light from a hot early universe, now cooled. A, C, and D are true, but none tells us the universe began hot and dense.

Part 5 · Every team · Mission Brief: Somewhere Else

Use it in your project

“What would it actually take to stand on this world and come home again, and which subsystem breaks first?”

  • Give every subsystem one driving number.
  • Compare two plans with weights set first.
  • Draw a sky you can defend with physics.
  • Log the number that killed each idea.
Open the Mission Brief project Project Library
The four Mission Brief deliverablesFour cards: an architecture brief drawn as linked boxes, a trade-study table, the sky seen from a planet's surface with its sun and a moon, and a field journal. architecture brief trade study sky from the surface field journal

Use it · Mission Brief · Mission architecture brief

Give every subsystem one driving number

Six subsystems of a Moon mission, each with its driving number An example mission to a Moon base, broken into six subsystems in order. Launch: leave Earth at 11.2 kilometres per second, Earth's escape velocity. Transit: 384,400 kilometres, with radio messages taking 1.3 seconds each way. Arrival and descent: almost no air, so no parachutes; rockets must do all the braking. Surface operations: a 14.8-day night that cools the ground to 95 K. Power and life support: about 14,200 kilowatt-hours to run 40 kilowatts through one night. Return: leave the Moon at 2.38 kilometres per second, its escape velocity. EXAMPLE: A MOON BASE 1 · Launch2 · Transit3 · Arrival, descent 4 · Surface ops5 · Power, life6 · Return 11.2 km/s384,400 km≈ no air 14.8-day night14,200 kWh2.38 km/s Earth's escape speed radio delay 1.3 s no parachutes: rocketsdo all the braking ground cools to 95 K per night at 40 kW the Moon's escape speed
Turn in
Mission architecture brief · Assessment Center, typed
Do
Real data on your destination first. Then each subsystem: its one driving constraint, as a number, and how you answer it.
Data
NASA Moon Fact Sheet · Mars Fact Sheet · all planets
Slides
Lunar night · Density · Orbit time · Light time

Use it · Mission Brief · Architecture trade study

Set the weights before you score

A trade study in three steps Step 1: split 100 percent of the weight among five criteria before scoring anything. The example split is crew safety 30, launch mass and cost 25, reliability 20, mission duration 15, and planetary protection and ethics 10. Step 2: score each option from 1 to 5 on each criterion, using evidence. Example options for a Moon base: option A, an equator base on sunlight and stored power, dark for 14.8 days at a time; option B, a crater-rim base near the south pole with a 40 kilowatt fission reactor, where NASA says higher ground gets longer periods of light. Step 3: the total is the sum of weight times score, and the recommendation must say what it gives up. 1 · Split 100% of the weight first crew safety 30mass, cost 25reliability 20time 15ethics 10 example weights · ethics includes planetary protection 2 · Score each option 1 to 5, from evidence A · Equator base sunlight plus stored power dark 14.8 days at a time store ≈ 14,200 kWh per night B · South-pole crater rim 40 kW fission reactor, under 6 t higher ground: longer light nearby craters: ≈ −235 °C 3 · Total = sum of (weight × score) Then name what the winner gives up, in one plain sentence.
Turn in
Architecture trade study · Assessment Center, typed, with a comparison table
Do
Fix the weights first. Score both options from evidence. State what your choice sacrifices.
Data
NASA Fission Surface Power · NASA Artemis Base Camp
Slides
Lunar night · Sun angle · Air and light

Use it · Mission Brief · Sky from the surface

Every object in your sky needs a physics reason

The same Sun from three surfaces Three noon skies, with the Sun drawn to the same scale. Earth: the Sun is 0.53 degrees wide in a blue sky, because air scatters blue light. Mars, 1.524 AU from the Sun: the Sun looks 0.53 divided by 1.524, about 0.35 degrees wide, gives 43 percent of Earth's sunlight, and sits in a hazy, reddish sky full of dust; the moon Phobos crosses the sky about three times a day. The Moon, 1 AU from the Sun: the Sun is 0.53 degrees wide, but the sky is black because there is almost no air, and Earth hangs in the sky. Earth Sun 0.53° wide blue: air scatters blue Phobos Mars Sun 0.35° · 43% the light hazy red: dust in the air Earth the Moon Sun 0.53° wide black: almost no air Sun's width = 0.53° ÷ distance in AU · sunlight = 1 ÷ distance²
Turn in
Sky from the surface · Studio Turn-In, image pages: the view plus its key
Do
State the local time. Key every element: Sun size, sky colour, moons and phases, stars.
Data
NASA Mars Facts · NASA Eyes on the Solar System
Slides
1 ÷ d² · Phases · Tilts

Use it · Mission Brief · Field journal

Log the number that killed each rejected idea

One journal entry in seven parts A journal page listing the seven parts of each day's entry: header, today's question, raw record, method log, sense-making, dead ends, and handoff. The dead-ends part is highlighted with an example: rejected a solar-only base at the equator, because the 14.8-day night would mean storing about 14,200 kilowatt-hours to keep 40 kilowatts running. 1234567 HeaderToday's questionRaw recordMethod logSense-makingHandoff date, day 3 of 7, team, your role one sentence this day settles numbers with units, as taken what you did, and why you changed it claim and evidence so far next step, open question Dead ends Rejected: a solar-only base at the equator. Killer number: 14.8 days dark = 14,200 kWh to store.
Turn in
Field journal — Mission Brief · Note Studio, one note titled with the project name
Do
One dated entry per project day, all seven parts, then a closing retrospective.
Focus
Mission design is a chain of eliminations. Your dead ends are evidence.
Slides
Lunar night · Formulas

Use it · Mission Brief · Your team's build

The slides your build and teach-back need

Moon Watch · telescope, crater tray, phase stage

Magnification, crater width per drop, dark half the turn.

Planet Builders · orbit table

Inner marbles lap faster; mark the frost line.

Star Lab · Sun meter, bench, fate wheel

Pinhole ratio ≈ 0.0093; 2× distance, ¼ the lux.

Galaxy Mappers · disk, sorter, stretcher, balloon

Sun 5.2 cm out; crests 2 → 3 cm.

Orbit & Starlight ExplorerReadouts are model evidence: “When we changed ___, the ___ changed.” Open the lab

Use it · The whole year

Earth in space sits under every project you built

Part 6 · Reference · Formula sheet

Every Module 6 formula on one page

Telescope

magnification = fobjective ÷ feyepiece

Light caught grows with diameter². Example

Noon Sun (Practice Gym)

altitude = 90° − L + δ

δ = +23.5° June · 0° equinox · −23.5° December. Beam spread = 1 ÷ sin(altitude). Example

Moon phase (Practice Gym)

every 45° east of the Sun = next phase

0 new · 90 first quarter · 180 full · 270 third quarter. Rises ≈ 1 h later per 15°. Example

Phase cycle and energy

1 ÷ (1/27.32 − 1/365.25) = 29.53 d

Night ≈ half the cycle. Energy (kWh) = power (kW) × time (h). Example

Kepler's third law

P² = a³

P in Earth years, a in AU. Example

Pinhole Sun

D = (image ÷ screen) × 150,000,000 km

Both lengths in the same unit. Example

Inverse square

brightness falls as 1 ÷ d²

Distance ratio = √(brightness ratio). Example

Luminosity

L ÷ LSun = (R ÷ RSun)² × (T ÷ TSun)⁴

Ratio form of L = 4πR²σT⁴. Example

Lifetime (lab and Gym model)

t = 10 billion yr ÷ M2.5

M in Suns; about a factor of two, 0.4 to 20 Suns. Example

Fate bands (Practice Gym)

< 0.5 Suns: white dwarf, no giant stage · 0.5–8: giant, planetary nebula, white dwarf · 8–20: supernova, neutron star · > 20: supernova, black hole. Slide

Hubble's law

v = H₀ × d

H₀ = 70 km/s per Mpc (Practice Gym; measured 67–74). d = v ÷ H₀. Example

Constants

c = 299,792 km/s · 1 ly = 9.46 × 10¹² km · 1 AU = 149.6 million km · 1 Mpc = 3.26 million ly · Sun 5,772 K · Earth's tilt 23.44° · Moon: 27.32 d orbit, 29.53 d phases, 5.1° orbit tilt.

Part 6 · Reference · Vocabulary

Module 6 words, in plain language

Telescope
A tool that gathers and focuses light from far away.
Focal length, magnification
Lens-to-focus distance; how many times wider things look.
Electromagnetic spectrum
All light, from radio waves to gamma rays.
Impact crater
A bowl blasted out by a rock from space.
Axial tilt
The 23.4° lean of Earth's spin axis.
Insolation
Sunlight energy reaching each square metre of ground.
Solar declination
The latitude where the noon Sun is straight overhead.
Phase
How much of the Moon's lit half faces Earth.
Elongation
The Moon's angle east of the Sun, seen from Earth.
Synodic month
One full cycle of phases: 29.53 days.
Lunar and solar eclipse
The full Moon in Earth's shadow; the new Moon's shadow on Earth.
Tide
The regular rise and fall of sea level.
Spring and neap tides
Biggest range (new, full moon); smallest (quarter moons).
Solar nebula
The spinning cloud of gas and dust that became the solar system.
Accretion
Grains and clumps sticking together and growing.
Planetesimal
A small rocky or icy body that built the planets.
Frost line
The distance from the Sun past which ice stayed solid.
Terrestrial planet, gas giant
Small rocky world; huge world of hydrogen and helium.
Density
Mass divided by volume.
Differentiation
A molten world sorting into layers by density.
Astronomical unit (AU)
Earth's average distance from the Sun: 149.6 million km.
Kepler's third law
P² = a³ for planets, in years and AU.
Asteroid
A rocky leftover, mostly between Mars and Jupiter.
Comet
An icy leftover that grows a tail near the Sun.
Meteoroid and meteor
A small rock in space; the streak it makes in air.
Nuclear fusion
Light nuclei joining into heavier ones and releasing energy.
Luminosity, apparent brightness
Total light given off; how bright it looks from here.
Kelvin (K)
Temperature counted from absolute zero: °C + 273.
H-R diagram
A plot of stars' temperature against luminosity.
Main sequence
The band of stars fusing hydrogen in their cores.
Red giant
A swollen, cool, bright old star.
Planetary nebula
The outer gas a dying Sun-like star sheds.
White dwarf
The hot, Earth-sized core left behind.
Supernova
The explosion of a massive star.
Neutron star, black hole
Supernova leftovers: an ultra-dense core; a core that traps light.
Light-year
How far light travels in a year: 9.46 trillion km.
Galaxy
Stars, gas, and dust held together by gravity.
Spiral galaxy
A flat disk with curved arms.
Elliptical galaxy
A smooth oval of mostly older stars.
Irregular galaxy
A galaxy with no clear shape.
Redshift
Light stretched to longer, redder wavelengths.
Hubble's law
Speed away = H₀ × distance.
Megaparsec (Mpc)
3.26 million light-years.
Big Bang theory
Expansion from a hot, dense start 13.8 billion years ago.
Cosmic microwave background
The oldest light we can see, now 2.7 K.

More wordsLook up any term in the Ascent Lexicon.

Part 6 · Reference · Trustworthy data

Real data for your mission, from the people who measure it

  • NASA NSSDCAPlanetary Fact Sheets

    Distance, size, density, gravity, tilt, and sunlight for every planet and the Moon.

  • NASA ScienceDaily Moon Guide

    Tonight's phase, and where the Moon is.

  • NASA ScienceEclipses

    Coming solar and lunar eclipses, and how they work.

  • NOAA Tides & CurrentsGalveston Pier 21

    Tide predictions and measured water levels on the Texas coast.

  • NOAA Global Monitoring LaboratorySolar Calculator

    Noon Sun height and day length for any place and date.

  • NASAEyes on the Solar System

    The sky from a planet or a spacecraft, for your sky view.

  • NASA JPLHorizons

    Where any planet or moon is, and how far away, on any date.

  • NASA Exoplanet ArchivePlanets around other stars

    Measured worlds such as Proxima Centauri b.

  • NASA ScienceStar Types

    Main sequence, giants, white dwarfs, neutron stars, and how each forms.

  • NASA Imagine the UniverseCosmic Connection to the Elements

    Which stars and events made which elements.

  • NASA ScienceUniverse overview

    The Big Bang, the first atoms, the background glow, the first stars.

  • NASAHubble images

    Galaxy photos for your sorting key.

Cite itWrite the source, the link, and the date you read it. Positions and tides change daily.

Part 6 · Ready for your project?

Three last checks

Why is Houston colder in January than in July?

Show the answer

B. Tilt lowers the noon Sun and shortens the day. A is backwards: Earth is closest in early January. The Sun's output barely changes (C). The Moon shades Earth only during a solar eclipse (D).

Two stars look equally bright. X is 3 times as far as Y. Compare their luminosities.

Show the answer

A. Distance alone would make X look 1/9 as bright, so to look equal it must give off 9 times the light. B forgets to square; C flips the ratio; D ignores distance.

A base runs 40 kW through a 14.77-day night. About how much energy?

Show the answer

C. 14.77 × 24 = 354 h, and 354 h × 40 kW ≈ 14,200 kWh. A multiplies days by kW with no hours; B is one Earth day; D covers the whole 29.5-day cycle.

You made it through Module 6

Now plan your trip somewhere else

Practice the math, test ideas in the lab, then build.

Mission Brief project Practice Gym · Module 6 Orbit & Starlight Explorer Module 6 page
A path from Earth to the Moon and backA dashed path arcs from Earth out to the Moon, labelled there, and a second dashed path returns, labelled and back. Small stars dot the sky. there and back