8.1.3a Orbital motion: planets, moons and satellites

Planets, moons and satellites: what orbits what

1. An orbit is the curved path an object follows around another object in space.
2. A planet is a large natural object that orbits a star; for example, Earth orbits the Sun.
3. A moon is a natural satellite that orbits a planet; our Moon orbits Earth.
4. A satellite is any object that orbits another object, and it may be natural or artificial.
5. An artificial satellite is a human-made object placed into orbit, most often around Earth.

Gravity holds an object in a circular orbit

1. Gravity is an attractive force between objects that have mass.
2. In a circular orbit, gravity provides a force directed towards the centre of the object being orbited.
3. An orbiting object is already moving forwards, and gravity constantly pulls it inwards.
4. This inward pull continually changes the direction of the object's motion, so its path curves into an orbit.
5. The Sun's gravity keeps Earth in orbit around the Sun.
6. Earth's gravity keeps the Moon, and also artificial satellites, in orbit around Earth.
7. Without this inward force the object would carry on in a straight line and leave its orbit.

Comparing planets, moons and artificial satellites

1. All three are similar in that they move in orbits.
2. In every case gravity provides the force that maintains the circular orbit.
3. Each one orbits a larger central object with a stronger gravitational pull.
4. They differ in what they orbit and in how they formed.
5. A planet is natural and orbits a star.
6. A moon is natural and orbits a planet, so it is a natural satellite.
7. An artificial satellite is human-made and is placed into orbit, usually around Earth.

8.1.3b Circular orbits: force, velocity and speed (HT)

Speed and velocity in a circular orbit

1. Speed tells you how fast an object moves and has size but no direction, so it is the magnitude of the velocity, $speed=|v|$.
2. Velocity is speed in a stated direction, so it is a vector.
3. A change in either the size or the direction of the motion counts as a change in velocity.

Gravity provides the centripetal force

1. A satellite in a circular orbit is pulled towards the centre of the body it orbits by the force of gravity.
2. This inward force is the centripetal force, the resultant force directed towards the centre of the circular path.
3. Gravity is not an extra force; in an orbit gravity provides the centripetal force.
4. Without it, the satellite would move off in a straight line along the tangent to the circle.

Changing velocity while the speed stays the same

1. At each point the satellite's velocity points along the tangent to the circular path.
2. Gravity acts at right angles ($90^{\circ }$) to this motion, pointing towards the centre.
3. A force acting at $90^{\circ }$ to the motion changes the direction of the velocity but not its magnitude.
4. So the direction keeps changing while the speed stays constant.
5. Because the velocity is changing, the satellite is accelerating, even though its speed does not change, since acceleration is any change in velocity.

Stable orbits link speed and radius

1. A stable circular orbit keeps a constant radius around the central body.
2. For each radius, the satellite needs a particular speed so that gravity bends its path by exactly the right amount.
3. If the speed changes but the radius stays the same, gravity bends the path by the wrong amount and the orbit is no longer stable.
4. So to stay in a stable orbit at a new speed, the orbital radius must also change: a faster satellite orbits at a smaller radius, and a slower one at a larger radius.
5. Speed and radius therefore cannot be changed independently in a stable orbit.