Question

QUESTION 1

Engineers wish to launch a satellite from the surface of the Moon. What is the minimum speed the satellite must have to escape the Moon’s gravity – that is, what is the escape velocity at the surface of the Moon? The Moon has a mass of 7.3x10^22 kg and a radius of 1.7x10^6 m.

	a.	1700 m/s
	b.	It depends on the mass of the satellite.
	c.	5.7x10^6 m/s
	d.	2400 m/s

10 points   

QUESTION 2

The satellite is guided to a circular orbit about the Sun at the same distance from the Sun as the Earth (1.5x10^11 m), but far away from the Earth (so only the Sun’s gravity is important). What is the satellite’s gravitational acceleration due to the Sun, which has a mass of 2.0x10^30 kg?

	a.	5.9 mm/s^2
	b.	9.8 m/s^2
	c.	8.9x10^8 m/s^2
	d.	It depends on the mass of the satellite.

10 points   

QUESTION 3

The satellite is guided to a circular orbit about the Sun at the same distance from the Sun as the Earth (1.5x10^11 m), but far away from the Earth (so only the Sun’s gravity is important). What is the satellite’s speed?

	a.	5.9 mm/s
	b.	3.0x10^4 m/s
	c.	8.9x10^8 m/s
	d.	It depends on the mass of the satellite.

10 points   

QUESTION 4

The satellite is guided to a circular orbit about the Sun at the same distance from the Sun as the Earth (1.5x10^11 m), but far away from the Earth (so only the Sun’s gravity is important). What is the satellite’s gravitational potential energy if it has a mass of 200 kg? The Sun has a mass of 2.0x10^30 kg.

	a.	-1.8x10^11 J
	b.	-8.9x10^8 J
	c.	2.9x10^14 J
	d.	-1.2 J

10 points   

QUESTION 5

The satellite is guided to a circular orbit about the Sun at the same distance from the Sun as the Earth (1.5x10^11 m), but far away from the Earth (so only the Sun’s gravity is important). The satellite is the stopped using orbital thrusters and allowed to fall to the Sun. What is the satellite’s speed when it reaches the surface of the Sun? The Sun has a mass of 2.0x10^30 kg and a radius of 7.0x10^8 m.

Hint: Use energy conservation. First consider the potential energy when it is at the Earth’s orbit, then equate this to the sum of the potential energy at the surface of the sun and the kinetic energy at the surface of the sun.

	a.	It will be going infinitely fast.
	b.	3.8x10^11 m/s
	c.	4.4x10^5 m/s
	d.	6.2x10^5 m/s

Answer 1

ANSWER 1:

The escape velocity is given by

Putting all the values in SI units

So, the escape velocity is 2400 m/s.

ANSWER 2:

The force of gravitation on the satellite due to the sun is

The acceleration due to gravity is

So, the acceleration due to gravitation is 5.9 mm/s².

ANSWER 3:

In a circular motion, the acceleration is given by

So, the speed of the satellite is 3 x 10⁴ m/s.

ANSWER 4:

The gravitational potential energy of the satellite is given by

So, the gravitational potential energy of the satellite is -1.8 x 10¹¹ J.

ANSWER 5:

The potential energy of the satellite at the surface of the sun is

The conservation of energy gives us

So, the velocity of the satellite at the surface of the sun is 6.2 x 10⁵ m/s.