You have three errors.

1) The 300 miles is above the surface of the earth, not from the center of the earth. If the astronaut is 300 miles above the earth and the radius of the earth is 3960 miles, the astronaut is 3960+ 300= 4260 miles from the center of the earth.

**I tried setting up a right triangle in a circle to find the distance from the surface of the earth to the location of the astronuat not realizing that it was given to be 300 miles. After reading your reply, I drew a picture to see where my error stemmed from.**
2) Your formula has

but you didn't square!

**Squaring would not have made a difference because I had the wrong information in the proportion.**
3) Since weight is

**inversely** proportional to the distance, you should have

Try

.

But that is NOT the 1.54 pounds. 300 miles is relatively small compared to 3960 so you really haven't gone a great distance, comparatively. And

**how** is the astronauts weight to be measured? Is there more to the problem you haven't told us?