### Question Description

A satellite has a mass of 106 kg and is located at ^{6}

The response you submitted has the wrong sign. J

(b) What is the magnitude of the gravitational force on the satellite?

N

## Explanation & Answer

Thank you for the opportunity to help you with your question!

G: Gravitational Constant = 6.673 × 10^-11

M: Mass of Earth = 5.9742 × 10^24 kg

m: mass of satellite = 1000 kg

r: distance to the center of the Earth = 6378000 + 2.03 × 10^6

(a) To determine gravitational potential energy (GPE) , you need to
select a reference level where the GPE is zero. Usually this is the
surface of the Earth and

GPE = weight × height <=== Equation A

because the weight is more or less constant. But for problems involving
planets and satellites, the reference level is usually at infinity and
we do not assume that the weight is constant. In that case,

GPE = -GMm / r <=== Equation B

Where r is the distance from the center of the Earth (the radius of the
Earth plus the altitude). If you are new to potential energy, you are
expected to use Equation A. If you are getting into more advanced
problems with orbital mechanics, you are expected to use Equation B.
I'll give you both answers:

GPE = weight × height

= (1000 kg)(9.8 N/kg)(2.03 × 10^6)

= 2.058 ×10^6 Joules <=== First answer to (a)

GPE = -GMm / r <=== Equation B

The radius of the Earth is 6378000 m, so r is 6378000 + 2.03× 10^6.

GPE = -(6.673 × 10^-11)(5.9742 × 10^24)(1000) / (6378000 + 2.03 × 10^6)

= -4.70 × 10^7 Joules <=== Second answer to (a)

(b) F = GMm / r²

= (6.673 × 10^-11)(5.9742 × 10^24)(1000) / (6378000 + 2.03 × 10^6)²

= 554.6 Newtons <=== Answer to (b)