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The question states:A satellite has a mass of 5850 kg and is in a circular orbit 4.1 × 105 m above the surface of a planet. The period of the orbit is 2.00 hours. The radius of the planet is 4.15 × 106 m. What would be the true weight of the satellite if it were at rest on the planet's surface?I'm unsure as to how to draw the free body diagram as well as solving the problem. Any help would be aappreciated!

Question

The question states:A satellite has a mass of 5850 kg and is in a circular orbit 4.1 × 105 m above the surface of a planet. The period of the orbit is 2.00 hours. The radius of the planet is 4.15 × 106 m. What would be the true weight of the satellite if it were at rest on the planet's surface?

I'm unsure as to how to draw the free body diagram as well as solving the problem. Any help would be aappreciated!

check_circleAnswer
Step 1

The equation for the time period of the satellite is given by

27 (R+h)
т
g
Here, T is the period of the satellite, R is the radius of the planet and g is the acceleration due to
planet's pull
Squaring both sides of the above equation and rearranging
472 (R+h
т?
T Rig 42R+h)
472 (R+h)
g =
т'R?
Substitute the numerical values in the above equation
- (4.15x10 m)
+(4.1x 10 m)
2
47T
g
2
3600s
(4.15x1061
2hx
m
= 4.19 m/s
help_outline

Image Transcriptionclose

27 (R+h) т g Here, T is the period of the satellite, R is the radius of the planet and g is the acceleration due to planet's pull Squaring both sides of the above equation and rearranging 472 (R+h т? T Rig 42R+h) 472 (R+h) g = т'R? Substitute the numerical values in the above equation - (4.15x10 m) +(4.1x 10 m) 2 47T g 2 3600s (4.15x1061 2hx m = 4.19 m/s

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Step 2

The equation for the true weight o...

W mg
Here, W is the true weight of the satellite and m is the mass of the satellite
Substitute the numerical values in the above equation
W (5850 kg) (4.19 m/s2)
- 2.45x104 N
help_outline

Image Transcriptionclose

W mg Here, W is the true weight of the satellite and m is the mass of the satellite Substitute the numerical values in the above equation W (5850 kg) (4.19 m/s2) - 2.45x104 N

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