DP Physics (last assessment 2024)

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

b.i.

[Maximum mark: 3]

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

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.i)

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

[3]

Markscheme

« $\frac{{m{v^2}}}{r} = \frac{{GMm}}{{{r^2}}}$ hence» $v = \sqrt {\frac{{GM}}{R}}$ . Also $v = \frac{{2\pi R}}{T}$

$m{\omega ^2}r = \frac{{GMm}}{{{r^2}}}$ hence ${\omega ^2} = \frac{{GM}}{{{R^3}}}$ ✔

uses either of the above to get ${T^2} = \frac{{4{\pi ^2}}}{{GM}}{R^3}$

uses $k = \frac{{4{\pi ^2}}}{{GM}}$ ✔

k = 9.2 × 10⁻¹³ / 9.3 × 10⁻¹³

Unit not required

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