Question

An astronaut weighs 800 N on the surface of earth. What is the weight of the astronaut 6.37 × 106 m above the surface of the earth? Assume the radius of earth is 6,378 km.

0.0 N

200 N

1,600 N

3,200 N
What is the answer and how is it found? Please explain the formula too

Answer 1

The universal formula for gravitational force (i.e. Weight) is

W = GMm/(r^2)
Where G is the gravitational constant 6.67*10^-11
M is the larger mass (in this case, the earth)
m is the smaller mass (the astronaut)
And r is the distance between the centers of mass of the objects.

In this case, you start from the given at the surface of the Earth:
800N=GMm/(6.378*10^6m)^2

*Since GMm will remain the same throughout, you don't actually need to solve any of them individually. Just solve for GMm as a single constant.*

After solving for GMm, plug that into the force at the new distance, which is the radius of the earth + height above the surface. Notice that the height above the surface given is the same as the radius of the earth.

W = GMm/(6.378*10^6*2)^2

Solving, you get W = 200 N

Answer 2

F=Gm1xm2d2 m1=mass of object
m2= mass of earth
G= Gravitational constant = 6.67300 × 10-11 [m3] [kg-1] [s-2]
d= distance from the center of the earth to the object
astronaut is 6.37 × 10^6 m above the surface of the earth
You sum that number to the radius of the earth 6,378 km.
This sum will give you "d". (d= 1275x10^7m.) 2.
The mass of Earth m2 = 5.97219 × 10^24 kilograms.
The mass of the astronaut is his weight difided by the force of gravity on the surface of the earth (9,8 m/s^2).
This is m1= 81.63kg.
"d", "m1", "m2" and G is a constant.
This is the force the earth attracts object
This is also his weight.
That is 200N.