Earth and the Solar System

The Earth spins on a tilted axis once a day (day and night) and orbits the Sun once a year; the tilt gives the seasons. The Moon orbits the Earth about once a month, showing phases as we see different amounts of its sunlit half. Eight planets, minor planets and comets orbit the Sun, held by gravity. Orbital speed is $v=\dfrac{2\pi r}T$ .

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Section 1 of 14

Learning objectives

Explain day and night, the seasons and the phases of the Moon.
List the planets in order and describe the other bodies in the Solar System.
Explain that gravity keeps planets, moons and comets in orbit.
Use $v=\dfrac{2\pi r}{T}$ and calculate light travel times.

Pause and think

When it's summer in Pakistan, it's winter in Australia. If summer happened because the Earth was closer to the Sun, would that be possible?

Section 2 of 14

Core idea

Start hereYou are moving at 30 km/s

Sitting still, you're actually travelling round the Sun at about 30 kilometres every second. Gravity is the invisible string that holds Earth, and every planet, on its curved path.

The big idea

Sun's gravity keeps planets in near-circular orbits. $v=\frac{2\pi r}T$ . Further planets: weaker gravity, slower speeds, longer years.

1. Orbits

The Moon orbiting the Earth

orbit (radians) = 0.0

Gravity pulls the Moon towards the Earth, constantly changing its direction, so it moves in a (nearly) circular orbit. One orbit takes about 27 days.

v=\frac{2\pi r}T

$r$: orbital radius (m).
$T$: orbital period (s).

Worked exampleEarth's orbital speed

$r=1.5\times10^{11}$ m; $T=3.16\times10^7$ s.

Goal: $v$ .
Strategy: Circumference ÷ period.

$2\pi(1.5\times10^{11})=9.42\times10^{11}\text{ m}$
One orbit.
$v=\frac{9.42\times10^{11}}{3.16\times10^7}=3.0\times10^4\text{ m/s}$
Divide.

Answer

30

km/s.

✓ CheckMatches the hook ✓.

Orbital speed v = 2πr / T for the planets

Further from the Sun means weaker gravity and slower orbits. Earth:

v=\dfrac{2\pi\times1.5\times10^{11}}{3.16\times10^7}\approx30

km/s.

Inner rocky planets; outer gas giants.
Light from the Sun takes ~8 minutes.
Light-year: $9.5\times10^{15}$ m.

Common misconceptionLight-year is time It's a distance.

Pause and think

Why does the Moon show phases?

Summary

Gravity provides the orbit.
$v=2\pi r/T$ .

Light-year: Distance light travels in one year.

HistoryCopernicus moves the Sun. For centuries people believed the Earth was at the centre of everything. In

1543

Nicolaus Copernicus published a model with the Sun at the centre, and in

1610

Galileo saw moons orbiting Jupiter through his telescope: clear proof that not everything circles the Earth.

Fun factYou're moving at 30 km/s. Sitting still, you're travelling round the Sun at about

30

km/s (over

100\,000

km/h) and spinning with the Earth at up to

1670

km/h. You don't feel it because everything around you is moving too.

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