Motion in the Universe

Why orbits happen

• The Moon does not fly off into space, and it does not crash into the Earth. Instead it keeps going around at a roughly constant distance
• The reason is gravity:
  • The Moon is pulled towards the Earth by gravitational attraction
  • But the Moon is also moving sideways (tangentially) very fast
  • The two effects combine to keep the Moon moving in a near-circular path around the Earth
• For a stable circular orbit:
  • The gravitational pull from the central body acts as a centripetal force, always pointing towards the centre of the orbit
  • This force constantly changes the direction of the orbiting body's velocity, but not its speed
  • The orbiting body falls towards the central body forever, but always misses, because its sideways motion carries it past the centre

Properties of any orbit

For any object in a stable orbit:

• The gravitational force always points towards the centre of the larger body
• The orbiting body moves in a roughly circular path (or, for some comets, a very stretched ellipse)
• The speed is constant for a circular orbit (varies for an elliptical one, see below)
• The orbiting body is always accelerating, because its direction is changing even when its speed is not

Orbits of planets, moons and comets

All three are caused by gravity, but they look quite different:

Planets around the Sun

• Each planet moves in a slightly elliptical orbit (close to circular) with the Sun at one focus
• All eight planets orbit in the same direction and in roughly the same plane (the plane of the Solar System)
• Each planet has a different orbital radius and therefore a different orbital speed and period:
  • Mercury is closest to the Sun, fastest, period ≈ 88 days
  • Earth has a period of 1 year (365.25 days)
  • Jupiter has a period of ≈ 12 years
  • Neptune is the furthest planet, slowest, period ≈ 165 years
• The closer a planet is to the Sun, the faster it orbits (because the Sun's gravitational pull is stronger near in), and the shorter its year

Moons around their planets

• Moons travel in near-circular orbits around their parent planet
• The closer the moon to the planet, the faster it orbits and the shorter its period, for the same reason
• The Moon takes about 27.3 days to orbit the Earth

Comets around the Sun

• Comets follow highly elliptical orbits, which are very stretched ovals
• They spend most of their time in the outer Solar System, moving slowly. When they swing close to the Sun they accelerate to very high speeds, then slow again as they head back out
• Many comets travel through space at a steep angle to the flat disc the planets occupy, and a few even loop round the Sun backwards (in the opposite sense to the planets)
• Comet Halley has a period of 76 years; some comets have periods of millions of years; some never come back at all (they are on hyperbolic trajectories that take them out of the Solar System)
• The speed of a comet changes a lot during one orbit: fastest at the closest point to the Sun, slowest at the furthest point