DP Physics (last assessment 2024)

Question 17N.2.SL.TZ0.5a

Date	November 2017	Marks available	[Maximum mark: 3]	Reference code	17N.2.SL.TZ0.5a
Level	SL	Paper	2	Time zone	TZ0
Command term	Determine	Question number	a	Adapted from	N/A

[Maximum mark: 3]

17N.2.SL.TZ0.5a

A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.

The satellite is orbiting the Earth at a distance of 6600 km from the centre of the Earth.

(a)

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

[3]

Markscheme

$\frac{{m{v^2}}}{r} = G\frac{{Mm}}{{{r^2}}}$

leading to T² = $\frac{{4{\pi ^2}{r^3}}}{{GM}}$

T = 5320 «s»

Alternative 2

« $v = \sqrt {\frac{{G{M_E}}}{r}}$ » = $\sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.0 \times {{10}^{24}}}}{{6600 \times {{10}^3}}}}$ or 7800 «ms^–1»

distance = 2 $\pi$ r = 2 $\pi$ x 6600 x 10³ «m» or 4.15 x 10⁷ «m»

«T = $\frac{d}{v} = \frac{{4.15 \times {{10}^7}}}{{7800}}$ » = 5300 «s»

Accept use of ω instead of v

Syllabus sections

Core

Core » Topic 6: Circular motion and gravitation » 6.1 – Circular motion

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

Core » Topic 6: Circular motion and gravitation

Question 17N.2.SL.TZ0.5a

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