Gravitation and Gravitational Fields

AI Thread Summary
A satellite is designed to orbit Earth at an altitude where the gravitational field strength is 4.5 N/kg, requiring calculations for its orbital distance, acceleration, and speed. The gravitational constant and Earth's mass are used to derive the orbital radius, which is found to be approximately 2.98 x 10^13 meters. The calculated orbital speed of 3.66 m/s raises concerns, as it is significantly lower than typical satellite velocities. Discussions highlight confusion about the correct formulas for velocity and acceleration, emphasizing the need to clarify the distinction between them. Overall, while part A is deemed correct, further assistance is needed to resolve the calculations for parts B and C.
Mary1910
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Homework Statement



A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5 N/kg.

a) Calculate the distance above the surface of Earth at which the satellite must orbit

b) Assuming the orbit is circular, calculate the acceleration of the satellite and its direction

c) At what speed must the satellite travel in order to maintain this orbit?

Homework Equations



F=G(m1)(m2)/(r)^2

v= √(G)(m) / (r)

The Attempt at a Solution



a)
G=6.67 x 10^-11 N•m^2/kg^2
m=5.98 x 10^24 kg
F=4.5 N/kg

F=G(m1)(m2)/(r)^2

r^2=G(m1)(m2) / (F)

r^2=(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (4.5 N/kg)
r=^2√8.863688889 x 10^13
r=2.98 x 10^13m

∴The distance above the surface of the Earth that the satellite must orbit is 2.98 x 10^13m or 2.98 x 10^10kmb)

v= √(G)(m) / (r)

v=√(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (2.98 x 10^13m)
v=√(9.98866 x 10^14) / (2.98 x 10^13m)
v=3.66 m/s

I don't think that its possible that this could be correct, after looking up a little bit about satellites I found that satellites have a much greater orbital velocity than this. I also don't understand how I am supposed to calculate the direction of the satellite with the information that has been given.

c) And finally, for c) wouldn't my answer just be the same as part b) ? Since I am only maintaining orbit I don't think I need to be concerned about an escape velocity.
Help with these would be really appreciated. Thank you.
 
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The second part asks you to find acceleration , not velocity .
Mary1910 said:
v= √(G)(m) / (r)
This is incorrect . Check the formula for ' v ' once again .

Hope this helps .
 
Qwertywerty said:
The second part asks you to find acceleration , not velocity .

This is incorrect . Check the formula for ' v ' once again .

Hope this helps .

I can't find any other formulas related to acceleration to solve this type of problem. Would it work if I solve for velocity and then divide velocity by time? Although, with this question I don't know if that would work either. Was part a) correct?
 
Do you know circular motion ?

Part A is fine .
 
Would a formula for planet/celestial orbit work for part c? Such as K=G(m1+m2) / (4π^2)
 
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