At what altitude above the Earth's surface would your weight be three-fifths of what it is at the Earth's surface? Assume re = 6.371 10^3 km.

If weight decreases as the inverse square of distance, then

3/5= (re/r)^2

where r is the distance from the center of earth to the spot you are interested.

altitude = r - re

1849.6

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How far (in meters) above the earth's surface will the acceleration of gravity be 18.0 % of what it is on the surface?

8225 km

To find the altitude above the Earth's surface where your weight would be three-fifths of what it is at the Earth's surface, you can use the equation you mentioned:

3/5 = (re/r)^2

where re = 6.371 * 10^3 km is the radius of the Earth and r is the distance from the center of the Earth to the spot you are interested in.

To solve for r, first take the square root of both sides of the equation:

(sqrt(3/5)) = sqrt(re/r)^2

Simplifying further, we get:

sqrt(3/5) = re/r

To isolate r, we can divide both sides of the equation by sqrt(3/5):

r = re / sqrt(3/5)

Now, we can substitute the given value for re = 6.371 * 10^3 km into the equation:

r = (6.371 * 10^3 km) / sqrt(3/5)

Evaluating the expression, we get the value of r.

Lastly, since altitude is defined as the distance from the Earth's surface (r) minus the Earth's radius (re), we can find the altitude:

altitude = r - re

Substitute the values of r and re into the equation to calculate the altitude.