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Gravitational fields

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Question 4

A scientific observation satellite orbits Mars at a height of 2.6×105 m2.6 \times 10^5\text{ m}2.6×105 m above Mars's surface.

The radius of Mars is 3.40×106 m3.40 \times 10^6\text{ m}3.40×106 m. The gravitational field strength g0g_0g0​ at Mars's surface is 3.71 N kg−13.71\text{ N kg}^{-1}3.71 N kg−1.

a.

Both the satellite and the instruments inside it are in free fall. Explain why this makes the instruments feel weightless.

[2]
b.

Calculate the value of the gravitational field strength ggg at the height of the satellite above Mars.

[3]
c.

The speed of the satellite in its orbit is 3.4 km s−13.4\text{ km s}^{-1}3.4 km s−1. Show that the period of the satellite in its orbit is about 110 minutes.

[2]
d.

Use the information in (b)(ii) and the data below to show that the root mean square (r.m.s.) speed of the nitrogen molecules inside the satellite is approximately 7 times smaller than the orbital speed of the satellite.

  • molar mass of nitrogen = 2.8×10−2 kg mol−12.8 \times 10^{-2}\text{ kg mol}^{-1}2.8×10−2 kg mol−1
  • temperature of nitrogen inside the satellite = 15∘C15^\circ\text{C}15∘C
[4]
e.

The satellite has arrays of solar cells on its wings. These solar cells charge batteries which power the satellite. The wings always face the Sun.

Use the data below and your answer to (b)(ii) to calculate the average power delivered to the batteries:

  • The total area of the cells facing the solar radiation is 180 m2180\text{ m}^2180 m2.
  • 12%12\%12% of the energy of the sunlight incident on the cells is stored in the batteries.
  • The intensity of solar radiation at the orbit is 590 W m−2590\text{ W m}^{-2}590 W m−2 outside of Mars's shadow and zero inside it.
  • The satellite passes through Mars's shadow for 40 minutes during each orbit.
[4]

Gravitational fields Questions

  1. A Level
  2. /Physics
  3. /Gravitational fields