Direct and Inverse Proportions

Question

The weight of an object is inversely proportional to the square of the distance from the object to the centre of the earth. An astronaut weighs 800 newtons (N) at sea level (6500 km from the centre of the earth).

a. Find the weight of the astronaut when he is orbiting 2.5 x 10 km above sea level.

b. Calculate how far above the centre of the earth the astronaut is when his weight is half of that at sea level

Answer 1

w = k/d^2

800= k/6500^2

k = 800x6500^2 = 800x42,250,000 = 3.38 x 10^10

w=3.38x10^10/6525^2=

about 794 newtons

weight is less as height is greater than sea level

25 +6500 km is slightly more than 6500,

so it's weight is slightly less than 800 N