Why does a planet in an elliptical orbit move faster when closer to the Sun?

According to Kepler's second law, equal areas must be swept in equal times; when the planet is closer to the Sun, it must travel faster to sweep the same area as when it is farther away.

State Kepler's third law of planetary motion.

The square of the orbital period of a planet is proportional to the cube of its orbital radius (T² ∝ r³).

What provides the centripetal force that keeps a planet in orbit around the Sun?

The gravitational force between the planet and the Sun provides the centripetal force required to maintain the orbit.

In the equation T² = (4π²/GM)r³, what does each symbol represent?

T is the orbital period, r is the orbital radius, M is the mass of the central body, and G is the gravitational constant.

OCR A-Level Physics A H556

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Gravitational Fields

Kepler's laws and orbital motion

3 things to know
Papers 1, 2 and 3

Overview

Recall questions on the three laws and on gravity supplying the centripetal force for an orbit.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

When deriving the orbital period equation, what is the first step involving forces?

Key term

State Kepler's first law of planetary motion.

Key term

What does Kepler's second law state about the motion of planets?

Questions from this subtopic

Each one with the model answer underneath.

1
State Kepler's first law of planetary motion.
Model answer
All planets move in elliptical orbits with the Sun at one focus.
2
What does Kepler's second law state about the motion of planets?
Model answer
A line joining a planet to the Sun sweeps out equal areas in equal intervals of time.
3
Why does a planet in an elliptical orbit move faster when closer to the Sun?
Model answer
According to Kepler's second law, equal areas must be swept in equal times; when the planet is closer to the Sun, it must travel faster to sweep the same area as when it is farther away.
4
State Kepler's third law of planetary motion.
Model answer
The square of the orbital period of a planet is proportional to the cube of its orbital radius (T² ∝ r³).
5
What provides the centripetal force that keeps a planet in orbit around the Sun?
Model answer
The gravitational force between the planet and the Sun provides the centripetal force required to maintain the orbit.
6
In the equation T² = (4π²/GM)r³, what does each symbol represent?
Model answer
T is the orbital period, r is the orbital radius, M is the mass of the central body, and G is the gravitational constant.

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