How Far Must a Rocket Travel from Earth to Weigh 1/100th of Its Surface Weight?

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Homework Help Overview

The problem involves determining the height above Earth's surface at which a rocket would weigh 1/100th of its weight on the surface. The context is rooted in gravitational force and its dependence on distance from the center of the Earth.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply gravitational equations but expresses confusion about their calculations and the expected result. Some participants suggest simplifying the problem by focusing on the relationship between the initial and final distances from the center of the Earth. Others question the correct interpretation of the relationship between the distances and the resulting weight.

Discussion Status

Participants are actively engaging with the problem, exploring different interpretations of the gravitational equations. Some guidance has been offered regarding the relationship between the distances, and there is an ongoing discussion about how to correctly express the height above the Earth's surface.

Contextual Notes

There is mention of potential confusion regarding whether to consider distances from the center of the Earth or from the surface, which is a critical aspect of the problem. The original poster also notes a discrepancy in their calculations compared to an expected answer.

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Homework Statement


How high above the surface of the Earth should a rocket be
in order to have 1/100 of its normal weight? Express your answer
in units of Earth radii.


Homework Equations


F=GMm/r2
F=mg


The Attempt at a Solution


r = √(( 6.67 x 〖10〗^(-11) x 5.97 x 〖10〗^24 )/0.098)
then divide by 6.37*106

I asked for help from one of my friends and he emailed me this but I think he might have messed somthing up. I keep getting a really big number.

I also know the answer its 9 radii but i don't understand how to get that answer.
 
Last edited:
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You don't need to use the actual mass of the Earth or the value of G.

You know that the weight is F = GMm/r^2
You know 'GMm' doesn't change,
So all you are asking is what do you have to do to 'r' to make 'r^2' 1/100 as big

ps. Careful with the final answer, r is from the centre of the Earth but the question asks for height above surface.
 
Last edited:
So i have to make r^2=1/10 of r^2?
 
yes - it migth help to label them rinitial and rfinal to avoid confusing yourself !
 
so how do i do that i tried r^2/10 its not right.
 
i think i got it, so I did r*10 then subtract 1 to get distance from Earth's surface not its center. Thnx for the help.
 
More formally you would write
ri2 = 100 rf2

Take square root of both sides, it also helps to know that sqrt(ab) = sqrt(a) * sqrt(b)
 

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