P8.3 Orbital motion, satellites and natural moons

Gravity as a centripetal force

Any object moving in a circle needs a centripetal force directed towards the centre of the circle. For planets orbiting the Sun, and moons orbiting planets, this centripetal force is provided by gravity.

The gravitational force depends on:

• The masses of both objects (F increases with mass)
• The distance between them (F decreases with distance squared — inverse square law)

Orbital speed and radius (Higher Tier)

For a circular orbit, the gravitational force equals the centripetal force:

F_grav = mv²/r

This means: the closer the orbit, the faster the orbital speed. A planet near the Sun moves much faster than a planet far from the Sun.

This is consistent with Kepler's third law: T² ∝ r³ (period squared proportional to radius cubed) — though you only need the qualitative idea for GCSE.

Natural satellites (moons)

Moons orbit planets in the same way that planets orbit the Sun. They are held in orbit by the planet's gravitational field. The Moon orbits Earth every ~27.3 days at about 384 000 km.

Artificial satellites

Artificial satellites are placed in specific orbits depending on their use:

• Low Earth orbit (LEO): ~200–2000 km altitude; fast orbit (~90 min); used for imaging, ISS, some communications.
• Geostationary orbit: ~36 000 km; period exactly 24 hours; stays above same point on Earth; used for TV broadcasting, weather, GPS.

Gravity and orbital mechanics

An object in orbit is in continuous free-fall towards the planet but moves forward fast enough that it keeps missing it. Gravity constantly changes the direction of the satellite's velocity (centripetal acceleration) without changing its speed (if the orbit is circular).

Exam tips

• "Orbital speed increases as radius decreases" — always justify using the centripetal force = gravity argument.
• Distinguish between natural moons (formed/captured) and artificial satellites (launched by humans).