What is the apparent weight of a 80-kg astronaut 2200 km from the center of the Earth's Moon in a space vehicle moving at constant velocity.

the apparent weight of the astronaut is 81.032 N { towards moon }

Explanation:

Given that;

Mass of astronaut m = 80 kg

Distance of spaceship from the Earth's moon r = 2200 km = 2200 × 10³ m

Acceleration due to gravity of the moon = GM/r²

where M is mass of the moon( 7.34767309 × 10²² kg )

gravitational constant G = 6.67 × 10⁻¹¹

So,

Acceleration due to gravity of the moon g is;

g  = [ (6.67 × 10⁻¹¹) × (7.35 × 10²²) ] / (2200 × 10³)²

g = 4.90245 × 10¹² / 4.84  × 10¹²

g = 1.0129 m/s²

now, we take the positive direction towards the moon if the spacecraft is moving with constant velocity, a = 0

The apparent weight is measured by the normal force FN

so,

∑F = ma

-FN + mg = ma

-FN + mg = 0

FN = mg

we substitute

FN = 80 × 1.0129

FN = 81.032 N { towards moon }

Therefore, the apparent weight of the astronaut is 81.032 N { towards moon }