Gravity 315km from Earth's Surface

In summary, the conversation discussed how to calculate the difference in gravity at different distances from Earth's surface and how to use Newton's law of gravitation to calculate acceleration. The correct equation to use is F = GMm/d^2 and additional information about the mass of the Earth is needed to solve the problem.
  • #1
shimizua
100
0

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

 
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  • #2
Try this equation: [tex] a = \frac{GM}{R} [/tex]

Where G = universal gravitational constant (6.76E-11)
M = mass of entity creating acceleration due to gravity
R = radius
 
  • #3
so would M be the mass of the Earth then?
 
  • #4
That's correct.
 
  • #5
Rake-MC said:
Try this equation: [tex] a = \frac{GM}{R} [/tex]
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?
 
  • #6
my teacher never gave us an equation for this one i am pretty sure.
 
  • #7
What about Newton's law of gravity?
 
  • #8
Fg=GMm/d^2?
 
  • #9
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?
 
  • #10
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
 
  • #11
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?
 

What is gravity at a distance of 315km from Earth's surface?

At a distance of 315km from Earth's surface, gravity is still present but it is significantly weaker compared to the surface. This is because gravity follows an inverse square law, meaning the further you are from the source (in this case, the center of the Earth), the weaker the gravitational force becomes.

How does gravity affect objects at 315km from Earth's surface?

Objects at 315km from Earth's surface will experience a weaker gravitational pull, meaning they will weigh less and have less gravitational potential energy compared to when they are on the surface of Earth. However, they will still orbit around Earth due to the centripetal force of gravity.

Can humans survive at a distance of 315km from Earth's surface?

Humans can survive at a distance of 315km from Earth's surface, but they would need to be in a spacecraft or space station with artificial gravity. The lack of gravity at this distance can have negative effects on the human body, such as muscle and bone deterioration, so it is not feasible for humans to live in this environment without proper equipment.

How does gravity at 315km from Earth's surface compare to other planets?

The strength of gravity at 315km from Earth's surface is similar to the strength of gravity on the surface of Mars. However, it is much weaker compared to the gravity on the surface of Earth, which is approximately 9.8 m/s^2. Other planets, such as Jupiter and Saturn, have much stronger gravitational forces due to their larger size and mass.

Is there a maximum distance at which gravity from Earth is still present?

Technically, gravity from Earth extends infinitely into space. However, its strength becomes negligible at extremely large distances. The point at which the gravitational pull becomes insignificant is known as the Hill sphere, which for Earth is approximately 1.5 million kilometers from its surface.

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