Q2 · 2024 · Paper 2Simple familiar6 marks
QUESTION 2 (6 marks)
In a distant solar system, a star, planet and spaceship are aligned as shown.
a)[3 marks]
Calculate the strength of the star’s gravitational field experienced by the spaceship. Show your working. Gravitational field strength = m s–2
b)[3 marks]
An observer on the planet measures the spaceship to be travelling directly towards the star at a speed of 1.9 × 108 m s–1. Calculate the distance between the spaceship and the star from the perspective of an astronaut on the spaceship. Show your working. Distance = m
WORKED SOLUTION
6 marksQCAA guide · typeset solution
ANSWER
See worked solution below.
Worked solution
11
30
11
11 2
2
20
11 2
4
6.67 10
1.9 10
(2.4 10
3.6
1.27 10
(6.0 10 )
3.5 10
10 )
GM
g
r
−
−
=
×
×
×
=
×
+
×
=
×
×
=
×
Gravitational field strength =
2
4
3.5 10 m s
−
−
×
(
)
(
)
2
8
11
2
8
2
0
2
1.9 10
6.0 10
1
3.0 10
1
v
L
L
c
×
×
×
−
=
−
=
×
Distance =
11
4.6 10
×
m
• shows mathematical reasoning that
relates to strength of a gravitational field
2
GM
g
r
=
[1 mark]
• recognises the distance is from centre of
star to centre of the spaceship [1 mark]
• calculates the gravitational field strength
[1 mark]
• recognises the scenario relates to length
contraction [1 mark]
• identifies proper length [1 mark]
• calculates the distance from the
spaceship’s frame of reference [1 mark]
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
How many marks did you earn?
Compare your working with the guide above.