DP Physics (first assessment 2025)

Question EXE.2.SL.TZ0.13

Date	Example questions Example questions	Marks available	[Maximum mark: 6]	Reference code	EXE.2.SL.TZ0.13
Level	SL	Paper	2	Time zone	TZ0
Command term	Determine, Outline, Show that	Question number	13	Adapted from	N/A

13.

[Maximum mark: 6]

EXE.2.SL.TZ0.13

(a)

Show that $T \propto r^{\frac{3}{2}}$ for the planets in a solar system where $T$ is the orbital period of a planet and $r$ is the radius of circular orbit of planet about its sun.

[2]

Markscheme

Equates centripetal force (with Newton’s law gravitation $m r ω^{2} = \frac{G M m}{r^{2}}$ )

AND

$T = \frac{2 π}{ω}$ ✓

leads to $T^{2} = r^{3} \times (\frac{4 π^{2}}{G M})$ hence result ✓

(b.i)

Outline what is meant by one astronomical unit (1 AU)

[1]

Markscheme

«mean» Distance from centre of Sun to centre of Earth ✓

Suitable ratio in terms of parsec and arcsecond ✓

(b.ii)

Pluto is a dwarf planet of the Sun that orbits at a distance of 5.9 × 10⁹ km from the Sun. Determine, in years, the orbital period of Pluto.

[3]

Markscheme

$T_{Pluto}^{2} = T_{Earth}^{2} \frac{r_{Pluto}^{3}}{r_{Earth}^{3}}$ used ✓

Earth orbital radius = 1.5 × 10¹¹ m (from AU) AND uses 1 earth year (in any units) ✓

247 years ✓

Syllabus sections

D. Fields

D. Fields » D.1 Gravitational fields

Question EXE.2.SL.TZ0.13

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