TBR Physics Passage VII Chapter 3 #49

[deleted388502]

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Feel like I'm missing something super easy here.

Two identical spacecraft are orbiting a planet. Spacecraft A is at an orbital radius of R, while Spacecraft B is at 3R. what is the ratio of the GPE of A to B?

The answer is 1:3...why is it not 3:1? Solution shows that GPE and r are inversely related and now I'm super confused

 

[DrknoSDN]

They are simplifying the equation:

That's the equation for gravitational potential energy at a radius r.
the mgh version is an approximation that is used to compare things at the surface of earth

Basically gravity gets weaker when you get farther from the mass producing the orbit.

This website (2 paragraphs) will explain.
http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html

 

[pizza1994]

They are simplifying the equation:

That's the equation for gravitational potential energy at a radius r.
the mgh version is an approximation that is used to compare things at the surface of earth

Basically gravity gets weaker when you get farther from the mass producing the orbit.

This website (2 paragraphs) will explain.
http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html

why cant we use the equation g=GM/r^2 and say g is gravitaonal potential energy and hence the relationship is 1:9?

 

[DrknoSDN]

why cant we use the equation g=GM/r^2 and say g is gravitaonal potential energy and hence the relationship is 1:9?

I believe that would only give you the relative acceleration due to the gravitational force at that radius. If it was asking for acceleration of gravity at the two different orbits you would want to use that equation. Different equation for potential energy tho.

 

[IslandStyle808]

Feel like I'm missing something super easy here.

Two identical spacecraft are orbiting a planet. Spacecraft A is at an orbital radius of R, while Spacecraft B is at 3R. what is the ratio of the GPE of A to B?

The answer is 1:3...why is it not 3:1? Solution shows that GPE and r are inversely related and now I'm super confused

Wait... What?

My book shows 3:1.

 

[deleted388502]

Wait... What?

My book shows 3:1.

must have diff versions. checked out a buddy of mine's version today and it had your answer as well.

 

[pepocho]

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