If your weight is w on the surface of the Earth, what is your weight at a height above the surface of the Earth equal to Earth's radius?
w
$w / 8$
$w / 4$
$w / 2$

Step 1 ：Given that your weight is \(w\) on the surface of the Earth, we want to find out what your weight would be at a height above the surface of the Earth equal to Earth's radius.

Step 2 ：The weight of an object is given by the formula: \(w = m*g\), where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity.

Step 3 ：The acceleration due to gravity is given by the formula: \(g = G*M/r^2\), where \(G\) is the gravitational constant, \(M\) is the mass of the Earth, and \(r\) is the distance from the center of the Earth.

Step 4 ：If you are at a height above the surface of the Earth equal to the Earth's radius, then the distance from the center of the Earth is \(2*r\). So the acceleration due to gravity at that height is: \(g' = G*M/(2*r)^2 = G*M/4*r^2 = g/4\).

Step 5 ：So your weight at that height is: \(w' = m*g' = m*g/4 = w/4\).

Step 6 ：\(\boxed{w/4}\) is the final answer. Your weight at a height above the surface of the Earth equal to the Earth's radius would be \(w / 4\).