DP Physics (first assessment 2025)

Question SPM.2.HL.TZ0.4

Date	May Specimen-2023	Marks available	[Maximum mark: 7]	Reference code	SPM.2.HL.TZ0.4
Level	HL	Paper	2	Time zone	TZ0
Command term	Determine, Draw, Outline, Show that	Question number	4	Adapted from	N/A

[Maximum mark: 7]

SPM.2.HL.TZ0.4

A satellite moves around Earth in a circular orbit.

(a)

Draw an arrow on the diagram to represent the direction of the acceleration of the satellite.

[1]

Markscheme

arrow normal to the orbit towards the Earth ✓

(b)

The following data are given:

Mass of Earth, M = 5.97 × 10²⁴ kg
Radius of Earth, R = 6.37 × 10⁶ m
Orbital period of the satellite, T = 5.62 × 10³ s

(b.i)

Kepler’s Third Law of orbital motion states that $T^{2} = k r^{3}$ where $k$ is a constant and $r$ is the orbital radius of the satellite.

Show that $k = \frac{4 π^{2}}{G M}$ .

[1]

Markscheme

use of $v_{orbital} = \frac{2 π r}{T}$ AND either $v_{orbital} = \sqrt{\frac{G M}{r}}$ or $\frac{m v_{orbital}^{2}}{r} = \frac{G M m}{r^{2}}$ correctly manipulated ✓