SOLUTION: The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut wei

Algebra ->  Real-numbers -> SOLUTION: The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut wei      Log On


   

Question 1050635: The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 202 pounds on the surface of the Earth, what will this astronaut weigh 200 miles above the Earth? Assume that the radius of the Earth is 4000 miles.
Found 2 solutions by josmiceli, rothauserc:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+202+=+k%2A4000%5E2+
+202+=+k%2A4%2A10%5E6+
+k+=+50.5%2A10%5E%28-6%29+
----------------------
+w+=+k%2A4200+
+w+=+50.5%2A10%5E%28-6%29%2A4200+
+w+=+2.121%2A10%5E5%2A10%5E%28-6%29+
+w+=+.212+
The astronaut would weigh .212 pounds
Check my work

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We use k, the constant of proportionality
:
202 = k / 4000^2
:
k = 202 * 4000^2
:
**************************************************************************
weight 200 miles above the earth = (202 * 4000^2) / 4200^2 = 183.22 pounds
**************************************************************************
: