Q27 · 2023 · Paper 1Simple familiar5 marks
QUESTION 27 (5 marks)
A satellite orbits a planet of mass 6.42 × 1023 kg at a height of 5000 km from the surface. The planet has a diameter of 6780 km. Determine the speed required for the satellite to maintain its orbit. Show your working.
WORKED SOLUTION
5 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
Sample response The
T 40° ste
Y GM
re = ee • pr
(3390x10* +5000x10°)? 6.67x107' x 6.42 x10” a
• de
re 4m? x5.91x10” ce
6.67x10"" x 6.42 x10"
=2.33x10' s
2ar
v=—
T
_ 22x8.39x10°
2.3310*
=23x10'ms™
Speed = 2.3x10? ms“ (to two significant figures)
e recognises the scenario relates to
- orbital mechanics [1 mark]
— circular motion [1 mark]
• provides appropriate mathematical reasoning
[1 mark]
e demonstrates correct substitution [1 mark]
e calculates the speed [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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