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GCSE level questions on the Earth in Space

Q9. A satellite is in a circular orbit around the Earth. The diagram below shows the velocity of the satellite at two different positions in the orbit.

(a) Explain why the velocity of the satellite changes as it orbits the Earth.

The satellite is being constantly pulled by gravity towards the Earth. It therefore experiences acceleration towards the centre of its circular path. Although its speed is constant when it is in a stable orbit - it is constantly changing direction as it undergoes the circular path. Velocity is a vector - it has two components - magnitude and direction. Although the magnitude is constant the direction is changing so the velocity is not constant, but is constantly changing.

[3 marks]

(b) The graph shows how the length of a satellite orbit depends on the height of the satellite above the Earth's surface.

 

A satellite orbits 300 km above the Earth's surface at a speed of 7.73 km/s.

Calculate how many complete orbits of the Earth the satellite will make in 24 hours.

From the graph we have orbit length as 42100 km

time for one orbit = 42100/7.73 seconds

time for one orbit = 5446 s

24 hours has 24 x 60 x 60 seconds = 86400s

So, in 86400 s it will orbit 86400/5446 times

= 15.86

Therefore it will not quite make 16 orbits - only 15 complete ones - in 24 hours.

[5 marks]

(c) In 1772, an astronomer called J Bode developed an equation to predict the orbital radii of the planets around the Sun.

The table shows Bode's predicted orbital radii and the actual orbital radii for the planets that were known in 1772.

Planet
Predicted orbital radius
in millions of kilometres
Actual orbital radius
in millions of kilometres
Mercury
60
58
Venus
105
108
Earth
150
150
Mars
240
228
Jupiter
780
778
Saturn
1500
1430

 

(i) The predicted data can be considered to be accurate. Give the reason why.

The predicted data is very close to the actual data.

[1 mark]

(ii) Bode used his equation to predict the existence of a planet with an orbital radius of 2940 million kilometres. The planet Uranus was discovered in 1781. Uranus has an orbital radius of 2875 million kilometres. Explain why the discovery of Uranus was important.

It supported the prediction (made by Bode) and therefore provides evidence that the equation is true/correct/ works/accurate

[2 marks]

(Total 11 marks)