Motion in the Universe

5 marks · Normal

The table below shows some data about gravitational field strengths for two planets and their effect on the orbits of their moons.

(a)

Planetary Data
Planet	Mass (Earth=1.0)	Radius (Earth=1.0)	Gravitational Field Strength (N/kg)
Earth	1.0	1.0	10
Jupiter	320	11	23

[1 mark]

(b)

Explain, using the data, why gravity is stronger at the surface of Jupiter than at the surface of Earth.

[2 marks]

(c)

The moon of Jupiter orbits at an average radius of 422,000 km and completes one orbit in 1.8 days. Calculate the average orbital speed of this moon in km/s (show all working).

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) Data as shown in table; no changes needed.

(b) Jupiter is much more massive than Earth (320 times), which increases gravity, even though it has a larger radius (11 times Earth's). The increase in mass more than makes up for the increase in radius, resulting in stronger surface gravity.

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Table filled in or interpreted as shown; data correct.

M1 (b) · 1 mark · Mentions effect of much larger mass and larger radius for Jupiter vs. Earth.

A1 (b) · 1 mark · States that mass difference outweighs radius difference, giving stronger gravity.

M1 (c) · 1 mark · Correct formula and conversions for periods and radius.

A1 (c) · 1 mark · Accurate calculation of orbital speed (in km/s) from values provided. (follow-through)

Worked solution

a) Data is as provided in the table, no changes needed.

b) Jupiter is 320 times more massive than Earth, which increases gravitational field strength. Although Jupiter is about 11 times larger in radius than Earth (which would decrease field strength), the large increase in mass more than compensates for the larger radius, resulting in a stronger gravitational field at its surface.

c) Orbital speed = (2\pi r)/T

r = 422,000 km; T = 1.8 days = 1.8 × 24 × 3600 = 155,520 s