An object in orbit is pulled towards the body it orbits by gravity, and that force points towards the centre of the orbit at every moment. This appears in questions about the Moon, planets, satellites and comets.
It belongs to space physics as a whole and uses ideas from forces and momentum.
Why does an orbit need a force at all?
An object keeps moving in a straight line at constant speed unless a resultant force acts on it. A planet moving in a circle is not moving in a straight line, so a resultant force must be acting.
That force is gravity from the Sun. It acts towards the Sun, which is the centre of the orbit.
The planet’s velocity is along the path, at right angles to the force. A force at right angles to the motion changes the direction but not the speed.
How do you calculate orbital speed?
For a circular orbit, the object travels one circumference in one orbital period.
- Find the circumference: 2πr, where r is the orbit radius.
- Put the radius in metres and the period in seconds.
- Use speed = distance ÷ time.
- Give the answer to a sensible number of significant figures, and state the unit.
Gravity is strong near a large mass and weaker far away, which is why planets closer to the Sun orbit faster than distant ones. Check the Cambridge syllabus for which relationships you need to recall and which are supplied.
Worked example
An invented planet orbits a star in a circle of radius 2.0 × 1011 m. One orbit takes 1.0 × 108 s. Find its orbital speed, and state the direction of the force on it.
Step 1, circumference: 2πr = 2 × π × 2.0 × 1011 = 1.26 × 1012 m.
Step 2, speed: v = 1.26 × 1012 ÷ 1.0 × 108 = 1.26 × 104 m/s.
Step 3, answer to 2 significant figures: about 1.3 × 104 m/s, which is roughly 13 km/s.
Step 4, force: gravity from the star, directed towards the star, which is the centre of the orbit.
Check: 1.26 × 1012 divided by 1 × 108 gives 1.26 × 104. The unit is metres per second because the distance is in metres and the time is in seconds.
The mistake to watch for
A common slip is to describe a second force pushing the planet forward along its path.
Mistaken answer: “The planet keeps moving because its forward force balances gravity, so the forces are equal.”
If the forces balanced, the resultant would be zero and the planet would move in a straight line.
The correction: there is one force, gravity, directed towards the centre. The planet already has motion, and it does not need a force to keep that motion going. The resultant force is the unbalanced pull towards the centre, and it keeps bending the path.
Check yourself
Try these, then open each answer.
1. State the direction of the force that keeps the Moon in orbit around Earth, and name the force.
Show answer
The force is gravity, directed towards the centre of Earth, which is the centre of the Moon’s orbit.
2. An invented satellite has an orbit radius of 4.0 × 107 m and a period of 8.0 × 104 s. Calculate its speed.
Show answer
Circumference = 2π × 4.0 × 107 = 2.51 × 108 m.
Speed = 2.51 × 108 ÷ 8.0 × 104 = 3.14 × 103 m/s, so about 3.1 × 103 m/s.
3. A comet moves on an elliptical orbit around the Sun. Where is it moving fastest, and why?
Show answer
It moves fastest when closest to the Sun. The gravitational pull is strongest there, and on the way in the comet gains speed as it moves towards the Sun.
Where this leads next
Once the force direction is clear, move on to reading a scale diagram of the solar system to see how large these orbits really are. For rounding your final answers sensibly, the bounds and rounding explainer is a useful check.
Some students get the calculation right but write explanations that invent extra forces. That is the kind of pattern a teacher can spot quickly in online one-to-one Physics tuition.