Using 6400 km as the radius on Earth, calculate how high above Earth's surface you would have to be in order to weigh 1/16th of your current weight. Show all work leading to your answer OR describe your solution using 3-4 complete sentences.

To solve this problem, we can use the concept of gravitational force and the formula for the weight of an object. The weight of an object is given by the formula W = mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity. Since we want to find the height at which the weight is 1/16th of the current weight, we can set up the following equation:

W/16 = mg'

where W is the current weight, m is the mass of the object, and g' is the acceleration due to gravity at the new height.

We know that the acceleration due to gravity is inversely proportional to the square of the distance from the center of the Earth, so we can write the equation as:

W/16 = m * (g0 / (1 + h/R))^2

where g0 is the acceleration due to gravity on the surface of the Earth, h is the height above the surface of the Earth, and R is the radius of the Earth.

Now, we can substitute the known values into the equation. The radius of the Earth is given as 6400 km (or 6400,000 meters), and the fraction of weight is 1/16th. We can assign the weight on the surface as W0, so W/16 = W0/16. Substituting these values, the equation becomes:

W0/16 = m * (g0 / (1 + h/R))^2

Simplifying the equation, we get:

16 = (1 + h/6400000)^2

Taking the square root of both sides, we have:

√16 = 1 + h/6400000

Simplifying further, we get:

4 = 1 + h/6400000

Subtracting 1 from both sides, we get:

3 = h/6400000

Multiply both sides by 6400000 to isolate h, resulting in:

h = 3 * 6400000

Calculating the height, we have:

h = 19200000 meters

Therefore, you would have to be approximately 19,200,000 meters above Earth's surface to weigh 1/16th of your current weight when the radius of Earth is 6400 km.