The Earth, the Sun and the Moon
Introduced| English | Meaning |
|---|---|
| Moon/muːn/ | The Earth’s natural satellite, orbiting it about once a month. |
| orbital speed/ˈɔːbɪtl spiːd/ | Speed along an orbit; for uniform circular motion, v = 2πr/T, where r is orbital radius and T is the period. |
| rotates/rəʊˈteɪts/ | rotates |
| orbits/ˈɔːbɪts/ | orbits |
| seasons/ˈsiːznz/ | The yearly cycle of climate caused by the tilt of the Earth’s axis as it orbits the Sun. |
| phases/ˈfeɪzɪz/ | The changing illuminated shapes of the Moon seen from Earth during its orbit. |
| period/ˈpɪərɪəd/ | The time taken for one complete oscillation or cycle. |
Days, months and years
- A day, a month and a year all come from motion in space.
- The Earth spins, the Moon 月球 circles us, and we circle the Sun.
- Let's see what each motion gives us — and how to find an orbital speed 轨道速率.
The spinning, orbiting Earth
- The Earth rotates 自转 on its axis once in about $24$ hours — giving day and night.
- It orbits 公转 the Sun once in about $365$ days — one year.
- Its axis is tilted, so each half of the Earth leans toward the Sun for part of the year — giving the seasons 季节.
The full Moon, Earth's natural satellite
Why the Moon changes shape
The Sun always lights half the Moon; the phase is simply how much of that lit half faces us as the Moon orbits — it is not Earth's shadow.
What causes day and night?
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The Earth rotates once in about 24 hours, so each place faces the Sun (day) then faces away (night).
What causes the seasons?
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The tilted axis means each hemisphere leans toward the Sun for half the year (summer) and away for the other half (winter).
The Moon
- The Moon orbits the Earth once in about one month.
- As it goes round, we see different amounts of its lit side — the phases 月相 (new, half, full).
- From shortest to longest: day (Earth's spin) < month (Moon's orbit) < year (Earth's orbit).
The Moon's lit half always faces the Sun, so as it orbits we see different amounts of it — new, half and full
Saturn and its rings, photographed by the Cassini spacecraft
Put these from the shortest time to the longest.
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Day (~24 hours) < month (~1 Moon orbit) < year (~365 days).
The phases of the Moon happen because we see different amounts of its lit side as it orbits.
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As the Moon orbits Earth, the fraction of its sunlit side that we can see changes, giving new, half and full moon.
Orbital speed
- One full orbit covers the circumference $2\pi r$, where $r$ is the orbit radius.
- The orbital speed is that distance divided by the period 周期 $T$ (the time for one orbit):
- The same equation works for planets, moons and satellites.
Mars, the red planet, one of the rocky inner planets
A satellite orbits at radius $r = 7.0 \times 10^6\ \text{m}$ with a period $T = 5800\ \text{s}$. What is its orbital speed, in m/s?
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$v = \dfrac{2\pi r}{T} = \dfrac{2\pi \times 7.0 \times 10^6}{5800} \approx 7600\ \text{m/s}$.
Compared with planets close to the Sun, the outer planets orbit:
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The Sun's gravity is weaker further out, so the outer planets move more slowly in their orbits.
Worked examples
1. The Earth orbits the Sun at $r = 1.5 \times 10^{11}\ \text{m}$ in $T = 3.15 \times 10^7\ \text{s}$ (one year). $v = \dfrac{2\pi r}{T} = \dfrac{2\pi \times 1.5 \times 10^{11}}{3.15 \times 10^7} \approx 3.0 \times 10^4\ \text{m/s}$.
2. The Moon orbits the Earth at $r = 3.8 \times 10^8\ \text{m}$ in $27.3$ days $= 2.36 \times 10^6\ \text{s}$. $v = \dfrac{2\pi \times 3.8 \times 10^8}{2.36 \times 10^6} \approx 1.0 \times 10^3\ \text{m/s}$.
Seasons come from the tilt of the Earth's axis, not from the Earth moving closer to the Sun. A day is one spin on the axis; a year is one orbit of the Sun.
You've got it
- Earth spins → day/night; orbits the Sun → year; tilt → seasons
- the Moon orbits Earth in ~1 month, giving its phases
- day < month < year
- orbital speed $v = \dfrac{2\pi r}{T}$
Write from an orbital speed of 3140 metres per second
- A satellite orbits at radius 4.0 times 10 to the 7 metres with period 8.0 times 10 to the 4 seconds. Use pi = 3.14.
- Find the orbital speed. Seasons come from the tilt of Earth's axis.
A satellite has orbital radius 4.0 times 10 to the 7 metres and period 8.0 times 10 to the 4 seconds. Using pi = 3.14, what is its orbital speed, and what causes the seasons?
2 times 3.14 times 4.0 times 10 to the 7, divided by 8.0 times 10 to the 4, is 3140 metres per second.
What is the orbital speed?
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2 pi r over T with pi = 3.14 is 3140 metres per second.