A Level · A2 · structured
A Level extension · Question 7
A Level extension · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 12
- Topics
- 2
- Answer
- Complete
A satellite is in a circular geostationary orbit about the Earth. The product GM for the Earth is 3.99 × 10¹⁴ m³ s⁻², and one day may be taken as 24 hours.
- (a)
Explain Explain what is meant by a geostationary orbit.
3 marks - (b)
Show (that) The gravitational force provides the centripetal force. Show that the radius of a geostationary orbit is approximately 4.2 × 10⁷ m.
4 marks - (c)
Calculate Calculate the linear speed of the satellite in this orbit.
2 marks - (d)
Explain A student suggests placing a geostationary satellite in orbit above London. Explain why this is not possible.
3 marks
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(a)
Explain Explain what is meant by a geostationary orbit.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the satellite has a period of 24 hours, equal to the Earth's period of rotation
- 2
it orbits in the same direction as the Earth's rotation, in the plane of the equator
- 3
so it remains vertically above the same point on the Earth's surface
(b)
Show (that) The gravitational force provides the centripetal force. Show that the radius of a geostationary orbit is approximately 4.2 × 10⁷ m.
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 = mrω², so GM = r³ω²
- 2
ω = 2π/T = 2π/86400 = 7.27 × 10⁻⁵ rad s⁻¹
- 3
r³ = GM/ω² = 3.99 × 10¹⁴ / (7.27 × 10⁻⁵)² = 7.55 × 10²²
- 4
r = 4.2 × 10⁷ m
(c)
Calculate Calculate the linear speed of the satellite in this orbit.
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
v = 2πr/T = 2π × 4.2 × 10⁷ / 86400
- 2
v = 3.1 × 10³ m s⁻¹
(d)
Explain A student suggests placing a geostationary satellite in orbit above London. Explain why this is not possible.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the centre of a circular orbit must be at the centre of the Earth, because that is where the gravitational force is directed
- 2
an orbit whose plane passes above London at a fixed latitude would have its centre away from the Earth's centre
- 3
so the satellite would have to be held up by some force other than gravity, which there is none to provide
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