Question

What is the Earth's gravitational force on you when you are standing on the Earth and when you are riding in the Space Shuttle 360 km above the Earth's surface? Answer as a fraction of the surface gravity of Earth. (The Earth's radius is 6400 km.)

Answer 1

Part A.

Earth's gravitational force on you when standing on earth

F1 = G*m1*m2/R^2

G = 6.67*10^-11, m1 = mass of earth = 5.98*10^24 kg

m2 = your mass = 70 kg (this value is different for everyone)

R = distance between you and center of earth = radius of earth = 6400 km = 6.40*10^6 m

So,

F1 = 6.67*10^-11*5.98*10^24*70/(6.40*10^6)^2

F1 = 681.6 N

Now when you are riding in space shuttle, then

F2 = G*m1*m2/R1^2

R1 = distance between you and center of earth = Re + H = 6400 km + 360 km = 6760 km

R1 = 6.76*10^6 m

So, Now

F2 = 6.67*10^-11*5.98*10^24*70/(6.76*10^6)^2

F2 = 610.98 = 611 N

Now fractional ratio of F2 and F1 will be:

F2/F1 = 611/681.6

F2/F1 = 0.896

F2 = 0.896*F1

Here F1 is force on earth, So

F2 = 0.896*F_earth

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