A gravatational homework question

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SUMMARY

The discussion revolves around a gravitational homework problem involving the calculation of height above Earth's surface where an object's weight decreases to 0.99 times its weight at sea level. The relevant equations include the gravitational force formula, where the acceleration due to gravity at sea level is 9.81 m/s², and the radius of the Earth is 6370 km. The user attempted to solve for height (x) using the equation 0.99mg = (Gm(me)/(6370 + x)²) and arrived at an approximate solution of 1000 km, prompting requests for verification and clarification of the calculation process.

PREREQUISITES
  • Understanding of gravitational force and weight calculations
  • Familiarity with the gravitational constant (G = 6.67 x 10^-11 N(m/kg)²)
  • Knowledge of basic algebra and equation manipulation
  • Concept of acceleration due to gravity and its variation with distance
NEXT STEPS
  • Review the derivation of gravitational force equations
  • Learn about gravitational potential energy and its relation to height
  • Explore the concept of weight variation with altitude in physics
  • Investigate the implications of gravitational changes in astrophysics
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and weight calculations, as well as educators seeking to clarify concepts related to gravity and height effects.

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Homework Statement


If an object is near the surface of the earth, the variation of its weight with distance from the center of the Earth can often be neglected. The accelertaion due to gravity at sea level is 9.81 m/s^2. The radius of the Earth is 6370 km. The weight of an object at sea level is mg, where m is its mass. At what height above the surface of the Earth does the weight of the object decrease to .99mg?


Homework Equations


I used .99mg= (Gm(me)/(6370 + x)^2) ... where G= 6.67 x 10^-11 and me= mass of the earth

The Attempt at a Solution



I used the formula above and solved for x getting an answer around 1000km, there is no way for me to check my solution... Any hints?
Thanks
 
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Can you show exactly how you got 'x'? Because x=1000km is a bit odd.
 

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