Write the equation that links gravitational and centripetal force for an orbit.

\frac{GMm}{r^2} = \frac{mv^2}{r}

Does orbital speed depend on the mass of the satellite?

No, the satellite's mass cancels; it depends on M and r only.

How does orbital speed change with orbital radius?

It decreases as r increases: v ∝ 1/√r.

State Kepler's third law.

T² is proportional to r³ for bodies orbiting the same central mass.

What is r in orbit equations?

The distance from the centre of the central body (planet radius plus height).

What is a geostationary satellite?

A satellite that stays above the same point on the Earth: equatorial orbit, same direction as the Earth's rotation, period of one sidereal day.

What is the orbital period of a geostationary satellite?

One sidereal day, 8.62 × 10⁴ s (about 24 hours).

Why do astronauts in the ISS feel weightless?

They and the station are in free fall with the same acceleration, so there is no contact force; gravity provides the centripetal force.

Give the angular speed form of the force equation.

\frac{GMm}{r^2} = m\omega^2 r with \omega = 2\pi/T

Why does a higher orbit have a longer period?

The satellite travels a longer circumference at a lower speed.

Orbital motionEdexcel International A Level Physics: Flashcards

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What provides the centripetal force for a satellite in orbit?

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What provides the centripetal force for a satellite in orbit?: The gravitational attraction between the satellite and the body it orbits.
Write the equation that links gravitational and centripetal force for an orbit.: $\frac{GMm}{r^2} = \frac{mv^2}{r}$
State the equation for orbital speed.: $v = \sqrt{\frac{GM}{r}}$
Does orbital speed depend on the mass of the satellite?: No, the satellite's mass cancels; it depends on M and r only.
How does orbital speed change with orbital radius?: It decreases as r increases: v ∝ 1/√r.
State the equation for orbital period in terms of radius.: $T^2 = \frac{4\pi^2 r^3}{GM}$
State Kepler's third law.: T² is proportional to r³ for bodies orbiting the same central mass.
What is r in orbit equations?: The distance from the centre of the central body (planet radius plus height).
What is a geostationary satellite?: A satellite that stays above the same point on the Earth: equatorial orbit, same direction as the Earth's rotation, period of one sidereal day.
What is the orbital period of a geostationary satellite?: One sidereal day, 8.62 × 10⁴ s (about 24 hours).
Why do astronauts in the ISS feel weightless?: They and the station are in free fall with the same acceleration, so there is no contact force; gravity provides the centripetal force.
Give the angular speed form of the force equation.: $\frac{GMm}{r^2} = m\omega^2 r$ with $\omega = 2\pi/T$
Why does a higher orbit have a longer period?: The satellite travels a longer circumference at a lower speed.

Exam questions on Orbital motion

The International Space Station (ISS) moves in a circular orbit at a height of 4.0 × 10⁵ m above the Earth's surface. The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. G = 6.67 × 10⁻¹¹ N m² kg⁻².
Calculate the time taken for the ISS to complete one orbit.2 marks
A geostationary communications satellite remains above the same point on the Earth's surface. The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m, and it rotates once in 8.62 × 10⁴ s (one sidereal day). G = 6.67 × 10⁻¹¹ N m² kg⁻².
Explain why a geostationary satellite must orbit in the plane of the equator.2 marks
Mars moves in an approximately circular orbit of radius 2.28 × 10¹¹ m around the Sun, which has mass 1.99 × 10³⁰ kg. G = 6.67 × 10⁻¹¹ N m² kg⁻². Take one year to be 3.16 × 10⁷ s.
Show that the orbital period T of a planet in a circular orbit of radius r around the Sun is given by T² = 4π²r³/GM, where M is the mass of the Sun.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).