Gravitational fields

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Question 19

An atmospheric research probe orbits Venus at a height of $4.5 \times 10^5\text{ m}$ above Venus's surface.

The radius of Venus is $6.05 \times 10^6\text{ m}$ . The gravitational field strength $g_0$ at Venus's surface is $kg−18.87\text{ N kg}^{-1}$ .

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

[2]

Calculate the value of the gravitational field strength $g$ at the height of the probe above Venus.

[2]

The speed of the probe in its circular orbit is $s−17.1\text{ km s}^{-1}$ . Show that the period of the probe in its orbit is about 96 minutes.

[3]

Use the information in (b)(ii) and the data below to show that the root mean square (r.m.s.) speed of the argon molecules inside the probe's instrument coolant chamber is approximately 16 times smaller than the orbital speed of the probe.

molar mass of argon = $4.0 \times 10^{-2}\text{ kg mol}^{-1}$
temperature of argon inside the probe = $27∘C27^\circ\text{C}$
molar gas constant $8.31\text{ J mol}^{-1}\text{ K}^{-1}$

[3]

The probe has arrays of solar cells on its external panels. These solar cells charge batteries which power the probe's electronics. The panels are designed to always face the Sun when not in shadow.

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

The total area of the cells facing the solar radiation is $m285\text{ m}^2$ .
$15%15\%$ of the energy of the sunlight incident on the cells is stored in the batteries.
The intensity of solar radiation at the orbit is $m−22600\text{ W m}^{-2}$ outside of Venus's shadow and zero inside it.
The probe passes through Venus's shadow for 32 minutes during each orbit.

[4]

Gravitational fields

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Question 19

An atmospheric research probe orbits Venus at a height of $4.5 \times 10^5\text{ m}$ above Venus's surface.

The radius of Venus is $6.05 \times 10^6\text{ m}$ . The gravitational field strength $g_0$ at Venus's surface is $kg−18.87\text{ N kg}^{-1}$ .

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

[2]

Calculate the value of the gravitational field strength $g$ at the height of the probe above Venus.

[2]

The speed of the probe in its circular orbit is $s−17.1\text{ km s}^{-1}$ . Show that the period of the probe in its orbit is about 96 minutes.

[3]

molar mass of argon = $4.0 \times 10^{-2}\text{ kg mol}^{-1}$
temperature of argon inside the probe = $27∘C27^\circ\text{C}$
molar gas constant $8.31\text{ J mol}^{-1}\text{ K}^{-1}$

[3]

The probe has arrays of solar cells on its external panels. These solar cells charge batteries which power the probe's electronics. The panels are designed to always face the Sun when not in shadow.

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

The total area of the cells facing the solar radiation is $m285\text{ m}^2$ .
$15%15\%$ of the energy of the sunlight incident on the cells is stored in the batteries.
The intensity of solar radiation at the orbit is $m−22600\text{ W m}^{-2}$ outside of Venus's shadow and zero inside it.
The probe passes through Venus's shadow for 32 minutes during each orbit.

[4]

Gravitational fields

Question 19

Gravitational fields Questions

Gravitational fields

Question 19

Gravitational fields Questions