Weight above the surface of the Earth

In summary, the problem involves finding the weight of an astronaut 6.37*10^6 km above the surface of the Earth. Using the equations F = G(m1)(m2)/(d)^2 and W=ma, the weight can be calculated by finding the forces acting on the astronaut at that height and using the mass of the astronaut and Earth. The final weight is determined to be 800.0514292 N or 81.63790094 kg. The altitude is essentially equal to the Earth radius, so the distance from the center of the Earth is doubled, causing the force magnitude to decrease to one-fourth of its original value.
  • #1
Sligh
10
0

Homework Statement



An astronaut weighs 800 N on the surface of the Earth. What is the weight of the astronaut 6.37*10^6 km above the surface of the earth?

Homework Equations



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

W=ma

The Attempt at a Solution



I am sure that I need the previous equations I listed, although I am not quite sure how to actually solve this problem. A solution to this type of problem would be most appreciated. Thanks!
 
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  • #2
you have your second equation wrong, it should read:
F = ma

G is constant, and you know d. So all you need are the two masses. Earth and astronaut.
 
  • #3
Thanks for the assistance. Here's what I figured ->

F = 6.67E-11*(81.632kg)(5.9742E24kg) / (6.37E6)^2

F=801.624N

W=81.8014kg
Is this alright? Thanks!
 
Last edited:
  • #4
Sligh said:
Thanks for the assistance. Here's what I figured ->

F = 6.67E-11*(81.632kg)(5.9742E24kg) / (6.37E6)^2

This would not give the weight at the point they are asking about. The d in the denominator of your equation is the distance to the center of the earth. So what would d be when the astronaut is at the height given?
 
  • #5
Ah, you are correct. Then I must add the radius of the Earth plus the distance at which the astronaut is above the Earth, yes?

Here's my new results:

F = 6.67E-11*(81.632)(5.9742E24) / (6.37E6 + 6378.1)^2

F = 800.0514292 N

W = 81.63790094 kg

Is that it?

Thanks.
 
  • #6
Sligh said:
Ah, you are correct. Then I must add the radius of the Earth plus the distance at which the astronaut is above the Earth, yes?

Here's my new results:

F = 6.67E-11*(81.632)(5.9742E24) / (6.37E6 + 6378.1)^2

Not quite; the Earth's radius is 6378.1 km, but you need to convert that to meters.
 
  • #7
Got it. Thanks a lot!
 
  • #8
You're welcome!

Notice in this problem that what they have done is set the altitude essentially equal to the Earth radius, so really the astronaut is doubling his distance from the center of the earth. In an inverse square law like gravity, if you double the separation, the force magnitude goes to one-fourth of its original value.
 

1. What is weight above the surface of the Earth?

Weight above the surface of the Earth refers to the force exerted by an object due to the Earth's gravity. It is the result of the mass of the object and the acceleration due to gravity, which is approximately 9.8 meters per second squared near the Earth's surface.

2. How is weight above the surface of the Earth different from weight on the surface?

The weight on the surface of the Earth is the force exerted by the Earth's gravity on an object when it is in direct contact with the surface. Weight above the surface, on the other hand, takes into account the distance between the object and the surface, which can affect the strength of the gravitational force.

3. Does weight above the surface of the Earth change at different altitudes?

Yes, weight above the surface of the Earth changes at different altitudes. This is because the distance between the object and the center of the Earth changes as altitude increases, and therefore the strength of the gravitational force changes as well.

4. How does weight above the surface of the Earth differ on other planets?

The weight above the surface of a planet is dependent on its mass and the strength of its gravitational force. Therefore, weight above the surface of other planets will vary based on their size and density. For example, an object that weighs 100 pounds on Earth would weigh 38 pounds on Mars due to its lower gravitational force.

5. Can weight above the surface of the Earth be negative?

No, weight above the surface of the Earth cannot be negative. Weight is a measure of the force of gravity, and gravity can only pull objects towards the center of the Earth. Therefore, weight will always be a positive value, even if an object is in free fall above the Earth's surface.

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