Magnitude of acceleration due to gravity

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Homework Help Overview

The problem involves calculating the magnitude of the acceleration due to gravity at a specific altitude above the Earth's surface, specifically at a height of 1.20 × 10^6 m. The context is centered around gravitational forces and orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of gravitational equations, including the formula for gravitational force and the relationship between height and gravitational acceleration. There is a focus on the correct interpretation of the radius in relation to the Earth's center and the height above the surface.

Discussion Status

Some participants have provided alternative approaches to calculating the acceleration due to gravity, suggesting different formulas and clarifying the definitions of variables involved. There is an acknowledgment of differing interpretations regarding the radius used in calculations.

Contextual Notes

Participants are navigating potential misunderstandings regarding the radius of the Earth and the height above it, as well as the implications of using different gravitational equations. The original poster's initial calculation appears to be incorrect, prompting further discussion and verification of the approach.

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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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