A setellite in Earth orbit has a mass of 91 kg and is at an altitude of 2.04 &#x00D7;<!-- × -

lurtzslikgtgjd

lurtzslikgtgjd

Answered question

2022-05-17

A setellite in Earth orbit has a mass of 91 kg and is at an altitude of 2.04 × 10 6 m. (Assume that U = 0 as r )(a) What is the potential energy of the satellite-Earth system?
J
(b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?
N
(c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no for
N

Answer & Explanation

Finnegan Zimmerman

Finnegan Zimmerman

Beginner2022-05-18Added 16 answers

Step 1
Given that,
Mass of satellite = 91 kg
Altitude h = 2.04 × 10 6   m
Step 2
We will use the formula of the potential energy at the altitude
The formula of the potential energy is
U = G M m r + h
Where M = mass of earth
m = mass of the satellite
G = gravitational constant
h = altitude
r = radius of the earth
We will use the formula of the gravitational force at the altitude
The formula of the gravitational force is
F g = G M m ( r + h ) 2
Step 3
(a). We need to calculate the potential energy of the satellite-earth system
Using the formula of the potential energy
U = G M m r + h
Put the value into the formula
U = 6.67 × 10 11 × 5.97 × 10 24 × 91 6.37 × 10 6 + 2.04 × 10 6 U = 4.30 × 10 9   J
(b). We need to calculate the magnitude of the gravitational force exerted by the earth on the satellite
Using the formula of the gravitational force
F g = G M m ( r + h ) 2
Put the value into the formula
F g = 6.67 × 10 11 × 10 24 × 91 ( 6.37 × 10 6 + 2.04 × 10 6 ) 2 F g = 512.3   N
(c). We know that,
According to Newton's third law,
The gravitational force exerted by the earth on the satellite is equal and opposite to the gravitational force exerted by the satellite on the earth.
We need to calculate the magnitude of the force exerted by the satellite on the earth
Using Newton's third law
F E s = F s E
Put the value into the formula
F E s = 512.3   N | F E s | = 512.3   N

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