How Far is the Satellite from Earth's Surface?

In summary: It's the distance from the center of the Earth.In summary, the Earth's radius is 6.86 e6 m and its mass is 5.98 e24 kg. A satellite is floating in space at a point where the Earth's gravitational acceleration is 3.2 m/s^2. To find the distance above the Earth's surface, we can use the formula Fg = Gmm/r^2, equating the gravitational force of attraction to the centripetal force. The mass of the satellite does not need to be known as it cancels out in the equation. Solving for the distance, we get R = √(GM/3.2), where R is the distance from the center of
  • #1
Rbethell16
10
0

Homework Statement


The radius of the Earth is 6.86 e6 m and the mass of the Earth is 5.98 e24kg. There is a satellite floating in space at a point where the Earth's gravitational acceleration is 3.2 m/s^2.

How far above the Earth's surface is the satellite?


Homework Equations


Fg = Gmm/r^2


The Attempt at a Solution


I know I need to find Fg - at least I think. But I don't know how to start...
 
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  • #2
Rbethell16 said:

Homework Equations


Fg = Gmm/r^2

The Attempt at a Solution


I know I need to find Fg - at least I think. But I don't know how to start...
The gravitational force of attraction provides the centripetal force. So you need to equate Fg and Fcentripetal (which you can just write as ma for this case).
 
  • #3
rock.freak667 said:
The gravitational force of attraction provides the centripetal force. So you need to equate Fg and Fcentripetal (which you can just write as ma for this case).

ma - ok, I have the acceleration, but I get confused as to which "m" i am using. My problem is the intuition with formulas
 
  • #4
Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?
 
  • #5
Rbethell16 said:
Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?

You don't need it! if you have

ma= GMm/r2

an 'm' (the mass of the shuttle) cancels out :wink:
 
  • #6
Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?
 
  • #7
Rbethell16 said:
Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?

Yes, but be aware of what that R is.
 

FAQ: How Far is the Satellite from Earth's Surface?

What is gravitational force?

Gravitational force is a fundamental force of nature that describes the attraction between objects with mass. It is responsible for keeping planets in orbit around the sun, and objects on Earth from floating away into space.

How is gravitational force calculated?

The strength of gravitational force is calculated using the formula F = G(m1m2)/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

What factors affect gravitational force?

The strength of gravitational force is affected by the masses of the objects and the distance between them. The larger the masses and the closer the objects are, the stronger the gravitational force.

How does the gravitational force of Earth differ from other planets?

The gravitational force of Earth is unique to its mass and distance from other objects, just like every other planet in our solar system. However, the strength of Earth's gravitational force is stronger than that of smaller planets like Mars or Venus, and weaker than that of larger planets like Jupiter or Saturn.

Can gravitational force be changed?

No, gravitational force cannot be changed. It is a fundamental force of nature that is constant and universal. However, the effects of gravitational force can be counteracted by other forces, such as the force of thrust from a rocket ship launching into space.

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