OCR A-Level Physics B H557
Planning
Implementing
Analysis
Evaluation
Practical Skills
Use of Apparatus and Techniques
Fundamental Data Analysis
Imaging and Signalling
Sensing
Mechanical Properties of Materials
Waves and Quantum Behaviour
Space, Time and Motion
Creating Models
Out Into Space
Our Place in the Universe
Matter: Very Simple
Matter: Hot or Cold
Electromagnetism
Charge and Field
Probing Deep Into Matter
Ionising Radiation and Risk
Out Into Space
Circular gravitational orbits
- 3 things to know
- Components 01, 02 and 03
Overview
Recall questions on gravity supplying the centripetal force, deriving orbital speed and the period–radius relation, why satellite mass drops out, geostationary and polar orbits, and decaying low orbits.
What you need to know
Answer each one before you reveal it.
State the relationship between the period and the radius of a circular orbit in words.
A satellite of orbital radius 6.77 × 10⁶ m travels at 7.7 × 10³ m s⁻¹. What is its period?
Questions from this subtopic
Each one with the model answer underneath.
- 1
How does the gravitational force provide the centripetal force for a circular orbit?
Model answer
The gravitational attraction GMm/r² acts towards the centre and is exactly the force mv²/r needed to hold the satellite on its circular path.
- 2
Derive an expression for the orbital speed of a satellite in a circular orbit of radius r.
Model answer
Setting GMm/r² equal to mv²/r and cancelling m gives v = √(GM/r).
- 3
Why does orbital speed not depend on the mass of the satellite?
Model answer
The satellite's mass appears on both sides of GMm/r² = mv²/r and cancels.
- 4
How does orbital speed vary with orbital radius?
Model answer
It is proportional to 1/√r, so a satellite in a larger orbit moves more slowly.
- 5
Derive the relationship between orbital period and orbital radius.
Model answer
Substituting v = 2πr/T into v² = GM/r gives T² = 4π²r³/GM.
- 6
State the relationship between the period and the radius of a circular orbit in words.
Model answer
The square of the period is proportional to the cube of the orbital radius.
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