SOLUTION: The weight of a body at or above the earths surface varies inversely as the square of the distance from the earths center. What does a 450 kg object weigh 500 km away for the earth

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Question 181207: The weight of a body at or above the earths surface varies inversely as the square of the distance from the earths center. What does a 450 kg object weigh 500 km away for the earths surface? a 450 kg object weighs 4410 Newtons at the surface of the earth. Newton is a unit of measure for weight. Use 6500 km as the radius of the earth in your calculations.
PLEASE GOD CAN SOMEONE HELP ME WITH THIS QUESTION AND GOD BLESS WHO EVER DOES
Answer by Edwin McCravy(6935) About Me  (Show Source):
You can put this solution on YOUR website!
>>...weight...varies inversely as the
square of the distance from the earth's center...<<

That says:

matrix%281%2C3%2CW%2C+%27=%27%2C+k%2Fd%5E2%29

>>...a 450 kg object weighs 4410 Newtons 
at the surface of the earth...<<

On the surface of the earth the distance d 
to the center of the earth is 6500 km, so
when d = 6500, then W = 4410. We substitute
that in the equation:

matrix%281%2C3%2CW%2C+%27=%27%2C+k%2Fd%5E2%29
matrix%281%2C3%2C4410%2C+%27=%27%2C+k%2F6500%5E2%29
matrix%281%2C3%2C4410%2C+%27=%27%2C+k%2F42250000%29

Now we can solve for k. So we multiply both 
sides by 42250000.

matrix%281%2C3%2C4410%2A42250000%2C%27=%27%2Ck%29

matrix%281%2C3%2C186322500000%2C%27=%27%2C+k%29

So we substitute 186322500000 for k in

matrix%281%2C3%2CW%2C+%27=%27%2C+k%2Fd%5E2%29

matrix%281%2C3%2CW%2C+%27=%27%2C+186322500000%2Fd%5E2%29

Now we read the question:

>>...What does a 450 kg object weigh 500 km
away for the earths surface?...<<

Since it's 500 km above the earth and it's 6500 km 
from the surface down to center of the earth, 
then the object is 500+6500 or 7000 km from 
the center of the earth.  So when d = 7000km,
we want to know what W is when d is 7000.

matrix%281%2C3%2CW%2C+%27=%27%2C+186322500000%2Fd%5E2%29
matrix%281%2C3%2C4410%2C+%27=%27%2C+186322500000%2F7000%5E2%29 
matrix%281%2C3%2CW%2C+%27=%27%2C+186322500000%2F7000%5E2%29
matrix%281%2C3%2CW%2C+%27=%27%2C+186322500000%2F49000000%29
matrix%281%2C3%2CW%2C+%27=%27%2C+3802.5%29

So it weighs 3802.5 Newtons.

Edwin