Cambridge International AS & A Level · 13 · structured
Derive an orbit, then test geostationarity
Circular gravitational orbits and geostationary conditions · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 8
- Topics
- 2
- Answer
- Complete
Starting with Newton's gravitational law, derive T² = 4π²r³/(GM). A satellite has r = 7.00 × 10⁶ m around Earth, GM = 3.99 × 10¹⁴ m³ s⁻². Determine T. Explain why a different satellite with a 24-hour period in a polar orbit is not geostationary, and state the remaining conditions.
- (a)
Derive the period-radius relation from the force balance.
3 marks - (b)
Determine the period at the stated radius.
2 marks - (c)
Explain the polar-orbit failure and state the geostationary conditions.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Derive the period-radius relation from the force balance.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
GMm/r² = m4π²r/T²; cancel m; T² = 4π²r³/(GM).
(b)
Determine the period at the stated radius.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
5.83 × 10³ s.
(c)
Explain the polar-orbit failure and state the geostationary conditions.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Circular and equatorial, west to east, with Earth's rotation period; a polar satellite changes latitude.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Set GMm/r² = m4π²r/T²; gravity provides the centripetal force.
- Cancel m and rearrange to T² = 4π²r³/(GM).
- T = 2π√[(7.00 × 10⁶)³/(3.99 × 10¹⁴)] = 5.83 × 10³ s.
- A polar satellite changes latitude relative to the ground. Geostationary requires a circular orbit above the Equator, west-to-east motion and the same rotational period as Earth, so ground position is fixed.
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