| Date | May 2018 | Marks available | 2 | Reference code | 18M.3.HL.TZ2.7 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Calculate | 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.
Calculate the distance of the event horizon of the black hole from its centre.
Mass of Sun = 2 × 1030 kg
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.
Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
Markscheme
boundary inside which events cannot be communicated to an outside observer
OR
distance/surface at which escape velocity = c
OWTTE
[1 mark]
mass of black hole = 7.2 × 1036 «kg»
«\(\frac{{2GM}}{{{c^2}}}\) =» 1 × 1010 «m»
[2 marks]
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]
