Q22 · 2021 · Paper 1Simple familiar3 marks
QUESTION 22 (3 marks)
A planet is orbiting a 3.38 × 1031 kg star. The radius of the orbit is 4.23 × 108 km. Calculate the average speed of the planet.
WORKED SOLUTION
3 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
Assume the planet is undergoing uniform circular motion.
𝐹= 𝑚𝑣2
𝑟
This is equal to the force of gravity.
𝐹= 𝐺𝑀𝑚
𝑟2
Equating these two equations and rearranging for velocity
gives:
𝑣= √𝐺𝑀
𝑟
𝑣= √6.67 × 10−11 × 3.38 × 1031
4.23 × 1011
v = 73 km s–1 or 73 005 m s–1
Average speed = 73 005 m s–1 (to the nearest whole
number)
• recognises the scenario relates to uniform
circular motion and universal gravitation
[1 mark]
• provides appropriate mathematical reasoning
[1 mark]
• calculates the average speed [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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