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Date May 2018 Marks available 2 Reference code 18M.3.HL.TZ2.7
Level Higher level Paper Paper 3 Time zone 2
Command term Discuss Question number 7 Adapted from N/A

Question

It is believed that a non-rotating supermassive black hole is likely to exist near the centre of our galaxy. This black hole has a mass equivalent to 3.6 million times that of the Sun.

Outline what is meant by the event horizon of a black hole.

[1]
a.i.

Calculate the distance of the event horizon of the black hole from its centre.

                                                                   Mass of Sun = 2 × 1030 kg

[2]
a.ii.

Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

M18/4/PHYSI/HP3/ENG/TZ2/07.b

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.

[2]
b.

Markscheme

boundary inside which events cannot be communicated to an outside observer

OR

distance/surface at which escape velocity = c

 

OWTTE

[1 mark]

a.i.

mass of black hole = 7.2 × 1036 «kg»

« 2 G M c 2 =» 1 × 1010 «m»

 

[2 marks]

a.ii.

wherever S-2 is in orbit, time observed is longer than 5.0 s

when closest to the star S-2 periodic time dilated more than when at greatest distance

Justification using formula or time is more dilated in stronger gravitational fields

 

[2 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.5 – General relativity (HL only)
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Option A: Relativity » Option A: Relativity (Additional higher level option topics)
Option A: Relativity

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