Example 1: Calculating a satellite's height above Earth
June 2020 · Paper 1P · Question 11(b)(i)
Question 1
This question is about satellites and their orbits.
KALPANA-1 was an artificial satellite used to monitor the weather.
The diagram shows the orbit of the satellite.
KALPANA-1 has an orbital speed of 3.1 km/s and completes one orbit in 24 hours.
Calculate the height of KALPANA-1’s orbit above the Earth’s surface.
[radius of Earth = 6400 km]
height above surface = ________ km
Final answer
The height of KALPANA-1’s orbit above Earth’s surface is 36,228 km (about 36,000 km to 2 significant figures).
Mark scheme points
- M1 Substitute the orbital speed, radius and time period into v = 2πr / T.
- M2 Convert 24 hours into 86 400 seconds.
- M3 Rearrange the equation and calculate the orbital radius: approximately 42 628 km.
- M4 Subtract Earth’s radius, 6400 km, to find the height above the surface.
Explanation
The equation gives the orbital radius measured from Earth’s centre. Convert the period to seconds so it matches the speed in km/s, then calculate that radius. Finally, subtract Earth’s radius to obtain the height above its surface.
T = 24 × 60 × 60 = 86 400 s
v = 2πr / T
r = vT / (2π)
= (3.1 km/s × 86 400 s) / (2π)
≈ 42 627.7 km
height = orbital radius − Earth’s radius
= 42 627.7 km − 6400 km
≈ 36 228 km
Common mistakes
- Using 24 as the time period without converting hours to seconds.
- Giving the orbital radius as the answer instead of subtracting Earth’s radius to find the height above the surface.