Magnitude of acceleration due to gravity

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SUMMARY

The magnitude of the acceleration due to gravity at a height of 1.20 × 106 m above the Earth's surface can be calculated using the formula g' = (Re2/r2) * g, where Re is the Earth's radius and g is the standard acceleration due to gravity at the surface. The correct calculation involves determining the total distance r from the center of the Earth, which is the sum of the Earth's radius and the height above the surface. The initial attempt using g = (G * ME * m) / r2 yielded an incorrect value due to not accounting for the Earth's radius in the total distance.

PREREQUISITES
  • Understanding of gravitational force equations, specifically W = G((ME m)/r2)
  • Familiarity with the concept of acceleration due to gravity (g)
  • Knowledge of the Earth's radius (approximately 6.37 × 106 m)
  • Basic algebra for manipulating equations and substituting values
NEXT STEPS
  • Research the derivation of the gravitational force equation W = G((ME m)/r2)
  • Learn how to calculate gravitational acceleration at various altitudes using g' = (Re2/r2) * g
  • Explore the implications of gravitational acceleration on satellite orbits
  • Investigate the effects of altitude on gravitational force and its applications in physics
USEFUL FOR

Students studying physics, particularly those focused on gravitational forces and satellite mechanics, as well as educators teaching concepts related to gravity and orbital dynamics.

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Homework Statement


Satellites are placed in a circular orbit that is 1.20 × 106 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?



Homework Equations


My book is saying that the relevant equations are:

W = G((ME m)/r2)

W = mg


The Attempt at a Solution


After looking at this post, I tried the formula g = MG/r^2. (M being the mass of the Earth)

g = ((6.67 x 10^-11)(5.97 x 10^24))/((1.20 x 10^6)^2)

This^ yielded 276.53 m/s^2, which is apparently wrong.
 
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g' = (Re^2/r^2)*g

r = Re + h where Re is the radius of the Earth and h is the height above it.

g = acceleration due to gravity on the earth

substitute the values given in the equation in that formula and you should get the answer for g'
 
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As Ronaldo said, ##r## is the distance of the object to the CM of earth. That means, as Ronaldo stated: $$r=1,20*10^6+r_{earth}$$
 
It looks like you guys are correct, because I got the answer correct and the book says the following...: http://twitpic.com/dx955g

Thank you!
 

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