Question on Gravity Keplers Laws?

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To calculate the initial acceleration of an object dropped from a height of 1.27E+7m, the correct approach involves using the gravitational formula with the distance from the Earth's center. The radius should include the Earth's radius (approximately 6.37E+6m) added to the height above the surface. It's crucial to ensure that the gravitational constant G is appropriately chosen based on the units used for mass and distance. After correcting the radius in the equation, the correct acceleration value of 1.09 was obtained. Proper unit conversion and understanding of gravitational principles are essential for accurate calculations.
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Question on Gravity Keplers Laws?

An object is dropped from a height of 1.27E+7m above the surface of the earth. What is its initial acceleration?

I thought I could use the equation for objects near the surface of the Earth in free fall which is :
g (or a) = GM / R^2
But this doesn't give me the right answer. Can anyone point me in the right direction?
 
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Welcome to PF!
You didn't use R=1.27E+7m, did you?
In that case, you'll get the wrong answer..
 
To give you a hint:
The "R" in the gravitation law is the DISTANCE FROM THE CENTER OF THE EARTH.
 
Becareful about what value you use for G.
The gravitational constant G comes in many flavors depending on your units.
You've used meters to represent the radius, and I'm not sure if you're expressing mass in g, kg, or Earth masses. So make sure you pick the right G, or convert your units for use with the G that you're using.
 
I got it! I added the Earth's radius (6.37E+6) to the radius above the Earth's surface and used it in my equation to get the right answer (1.09). Thank you very much for the help!
 
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