OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) the relationship for Kepler’s third law T 2 ∝ r 3 applied to systems…
Full specification wording
Planetary motion: (d) the relationship for Kepler’s third law T 2 ∝ r 3 applied to systems other than our solar system
Kepler's third law states that T² is proportional to r³ for any object orbiting a central mass under gravity.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 5
Study notes
From the checked teaching notes for this specification point.
The idea
Kepler's third law states that T² is proportional to r³ for any object orbiting a central mass under gravity. This applies not only to planets orbiting the Sun but also to moons orbiting planets, satellites orbiting Earth, and exoplanets orbiting distant stars. For a moon orbiting Jupiter, T² ∝ r³ with the constant of proportionality depending on Jupiter's mass. Similarly, for a satellite orbiting Earth, the constant depends on Earth's mass. The law allows comparison of orbital periods and radii for different systems, provided the central mass is the same. For example, if two moons orbit the same planet, the ratio T₁²/T₂² equals r₁³/r₂³. This relationship is used to determine masses of astronomical bodies from observed orbits.
What earns the marks
- State that T² ∝ r³ applies to any system where a smaller body orbits a larger central mass.
- Give examples such as moons orbiting planets, artificial satellites orbiting Earth, or exoplanets orbiting stars.
- Explain that the constant of proportionality depends on the mass of the central body.
- Use the ratio T₁²/T₂² = r₁³/r₂³ for objects orbiting the same central mass.
- Apply the law to determine the mass of a central body from orbital data of an orbiting object.
Common mistakes and how to put them right
Assuming Kepler's third law only applies to planets in the solar system.
Put it right by recognising it applies to any gravitational orbit.
Using the mass of the orbiting body instead of the central body when calculating the constant.
Put it right by using the central mass.
Forgetting that the law assumes circular orbits and that the central mass is much greater than the orbiting mass.
Put it right by stating these assumptions.
Exam tips
- When comparing two orbits around the same central body, use the ratio form to avoid calculating the constant.
- Ensure r is measured from the centre of the central body, not from its surface.
- Remember that T must be in seconds and r in metres for calculations.
Try the lesson
The start of the Planetary motion: (d) the relationship for Kepler’s third law T 2 ∝ r 3 applied to systems other than our solar system lesson, made from checked teaching notes for this specification point.
Listen
Kepler's third law states that T² is proportional to r³ for any object orbiting a central mass under gravity. This applies not only to planets orbiting the Sun but also to moons orbiting planets, satellites orbiting Earth, and exoplanets orbiting distant stars. For a moon orbiting Jupiter, T² ∝ r³ with the constant of proportionality depending on Jupiter's mass. Similarly, for a satellite orbiting Earth, the constant depends on Earth's mass. The law allows comparison of orbital periods and radii for different systems, provided the central mass is the same. For example, if two moons orbit the same planet, the ratio T₁²/T₂² equals r₁³/r₂³. This relationship is used to determine masses of astronomical bodies from observed orbits. A strong answer earns marks for these points. State that T² ∝ r³ applies to any system where a smaller body orbits a larger central mass. Give examples such as moons orbiting planets, artificial satellites orbiting Earth, or exoplanets orbiting stars. Explain that the constant of proportionality depends on the mass of the central body. Use the ratio T₁²/T₂² = r₁³/r₂³ for objects orbiting the same central mass. A common slip: Assuming Kepler's third law only applies to planets in the solar system. Instead, recognising it applies to any gravitational orbit. Exam tip: When comparing two orbits around the same central body, use the ratio form to avoid calculating the constant.
See it
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