DP Physics (last assessment 2024)

Question 18N.2.HL.TZ0.8b.ii

Date	November 2018	Marks available	[Maximum mark: 2]	Reference code	18N.2.HL.TZ0.8b.ii
Level	HL	Paper	2	Time zone	TZ0
Command term	Calculate	Question number	b.ii	Adapted from	N/A

b.ii.

[Maximum mark: 2]

18N.2.HL.TZ0.8b.ii

There is a proposal to place a satellite in orbit around planet Mars.

The satellite is to have an orbital time T equal to the length of a day on Mars. It can be shown that

T² = kR³

where R is the orbital radius of the satellite and k is a constant.

(b.ii)

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

[2]

Markscheme

${R^3} = \frac{{{T^2}}}{k} = \frac{{{{\left( {8.9 \times {{10}^4}} \right)}^2}}}{{9.25 \times {{10}^{ - 13}}}}$ R = 2.04 × 10⁷ «m» ✔

v = « $\omega r = \frac{{2\pi \times 2.04 \times {{10}^7}}}{{89000}} =$ » 1.4 × 10³ «m s^–1»

v = « $\sqrt {\frac{{GM}}{R}} = \sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.4 \times {{10}^{23}}}}{{2.04 \times {{10}^7}}}} =$ » 1.4 × 10³ «m s^–1» ✔

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Core

Core » Topic 6: Circular motion and gravitation » 6.2 – Newton’s law of gravitation

Core » Topic 6: Circular motion and gravitation

Question 18N.2.HL.TZ0.8b.ii

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