PhysicsChapter 1: Gravitation
Orbital Period and Kepler Relation
The orbital period
Definition
The orbital period is the time required for a satellite to complete one full orbit.
Formula / Key Relation
For circular orbit: distance travelled in one revolution: 2πr Therefore: v = 2πr/T From orbital velocity: v = √(GM/r) Equating: 2πr/T = √(GM/r) Squaring and rearranging: T² = 4π²r³GM Therefore: **T² ∝ r³ for satellites orbiting the same central mass. This is the circular-orbit form of Kepler’s third law. T = 2π√(r³/GM) T² ∝ r³**
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Review the key facts, formulas and checks before you move on.Orbital Period and Kepler Relation
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KEPLER 3
- `T² ∝ r³`
60-second revision
- Period grows rapidly with orbital radius.
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