# Calculate the force of gravity on a spacecraft 12800 km (2 earth radii) above the Earth’s surface if…?

its mass is 1700 kg.

• G = 6.67*10^-11

M = mass of earth = 5.97*10^24 kg

m = mass of spacecraft = 1700 kg

r = distance measured form earth = 6400 km + 12800 km = 19200 km = 19200000 m

F = GMm/r^2

F = 1.83 x 10^3 N

RE:

Calculate the force of gravity on a spacecraft 12800 km (2 earth radii) above the Earth’s surface if…?

its mass is 1700 kg.

• Earth Radius Km

• Here’s a quick and dirty solution that can avoid having to look up G and the mass of the Earth M.

From w = GmM/R^2; where R = r + 2r = 3r is the orbiting range of the craft of mass m = 1700 kg and r is Earth’s radius; we see that W/w = GmM/r^2//GmM/R^2 = (9r^2/r^2) = 9; so that the craft’s weight on the surface, where g = 9.81 m/sec^2 is W = mg = 9w; so that, at R = 3r, w = W/9 = mg/9 = 1700*9.81/9 = ? is the weight of the craft at three times the Earth’s radius. You can do the math, but we can easily see that the weight in orbit will be 1/9 its weight on the surface.

My point is this…the best way to solve problems where similar factors are being compared at different values (like W and w) is to use the ratio (like W/w = 9) because most factors (like M and G) will cancel out.

• I believe it’s one ninth.

P.S. Do you happen to be in grade 11 physics?