Calculate Distance Above Earth's Surface: 1.4x Radius

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SUMMARY

The discussion centers on calculating the distance above Earth's surface where gravitational force is reduced to 18% of its value at the surface. The user initially calculated a distance of 1070 meters but was confused about expressing this distance as a multiple of Earth's radius. The correct answer, as referenced in the textbook, is 1.4 times the Earth's radius (1.4 Re), which equates to approximately 8.9 million meters. This indicates that the distance is significantly greater than the initial calculation, emphasizing the importance of understanding ratios in gravitational contexts.

PREREQUISITES
  • Understanding of gravitational force equations
  • Familiarity with the concept of Earth's mass and radius
  • Basic algebra for manipulating equations
  • Knowledge of ratios and multiples in mathematics
NEXT STEPS
  • Study gravitational force calculations using Newton's Law of Universal Gravitation
  • Explore the concept of ratios and how they apply to physical measurements
  • Learn about gravitational fields and their variations with distance
  • Investigate the significance of expressing distances in terms of multiples of a reference value
USEFUL FOR

Students in physics or engineering, educators teaching gravitational concepts, and anyone interested in understanding the implications of distance in gravitational calculations.

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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