Calculate Distance Above Earth's Surface: 1.4x Radius

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Homework Help Overview

The problem involves calculating the distance above the Earth's surface where the gravitational force on an object is reduced to 18% of its value at the surface. The context is centered around gravitational force and its relation to distance from the Earth's center, specifically expressed as a multiple of Earth's radius.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up an equation relating gravitational force at two different distances but expresses confusion regarding the interpretation of "a multiple of Earth's radius." Other participants question the meaning of "multiple" and explore its implications in the context of the problem.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the terminology used in the problem. There is an exploration of the significance of expressing the distance as a multiple of Earth's radius, but no consensus has been reached on the interpretation or the calculations presented.

Contextual Notes

Participants are navigating the definitions and implications of terms used in the problem, particularly regarding ratios and multiples. The original poster's calculations are presented, but there is uncertainty about their correctness and how they relate to the expected answer in the textbook.

Vesper89
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At a certain distance above the surface of the Earth, the graviational force on an object is reduced to 18% of its value at Earth's surface. Determine this distance and express it as a multiple of Earth's radius.

FYI the Earth's mass is 5.98x10^24 kg
and the Earth's radius is 6.38x10^6 m

What I did was this: Gmm/r² = (Gmm/r²)(9/50) The left side is the gravitational force on the object at the surface of the Earth and the right side is %18 of that force (radius is unkown). Since Gmm is constant in both i came up with:

1/r² = 9/50r²
1/6.38x10^6 = 9/50r²
r = 1070m

But I don't understand what they mean in by a multiple of Earth's radius. In the back of my book the answer is 1.4 Re. Is my answer wrong? Or do I just need to take it another step? Thanks for any help!
 
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DO NOT PUT IN THOSE MEANINGLESS FIGURES!

Instead:
1. What is meant by a multiple?
In particular: In SYMBOLS, what is a multiple of the Earth's radius?
 
I assume its a ratio...in the back of the text the answer is 1.4 Re
(r subscript e...Radius earth) I'm not sure what it means or its significance:frown: .
 
What does it mean to multiply?

Do you think that has anything to do with the word "multiple"??
 

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