A satellite has a mass of 106 kg and is located at 2.03 106 m above the surface

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A satellite has a mass of 106 kg and is located at 2.03  106 m above the surface of Earth.

(a) What is the potential energy associated with the satellite at this location?
The response you submitted has the wrong sign. J

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

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Explanation & Answer

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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)

Please let me know if you need any clarification. I'm always happy to answer your questions.

qnex xavtug (29)
UT Austin

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