Gravity 315km from Earth's Surface

[shimizua]

Homework Statement

You are explaining to friends why astronauts feel weightless orbiting in the space shuttle, and they respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn't so by calculating how much weaker gravity is 315km above the Earth's surface in terms of g. Do not enter units.

Homework Equations

so i know that the further you get from Earth the less gravity there will be and that is why they feel weightless but i don't really know how to express that as an equation

The Attempt at a Solution

 

[Rake-MC]

Try this equation: $$a = \frac{GM}{R}$$

Where G = universal gravitational constant (6.76E-11)
M = mass of entity creating acceleration due to gravity
R = radius

 

[shimizua]

so would M be the mass of the Earth then?

 

[Rake-MC]

That's correct.

 

[D H]

Try this equation: $$a = \frac{GM}{R}$$

Don't try that equation.

Rake-MC, you are not supposed to give complete answers to a homework problem. You especially are not supposed to give completely wrong answers to a homework problem.

shimizua, what equations were you taught in your class?

 

[shimizua]

my teacher never gave us an equation for this one i am pretty sure.

 

[D H]

What about Newton's law of gravity?

 

[shimizua]

Fg=GMm/d^2?

 

[D H]

That's it. How do you compute acceleration given the force acting on a body? Use that on Newton's law of gravitation to recast Newton's law of gravitation in terms of acceleration rather than force. Can you solve the problem now?

 

[shimizua]

k so to get acceleration it is change of v over change in d. or would i use the original equation that Rake had up with Newtons law of gravity. I am am still confused

 

[D H]

Rake's equation is wrong. It doesn't even have the right units.

I gave you rather explicit instructions. I'll spell them out.

1. You are given a force F acting on some object of mass m. What is its acceleration?
2. You already gave the Newton's law of gravitation. Apply the equation I asked you to supply in step 1 to Newton's law of gravitation. What is the result?
3. What other information do you need to solve the problem?