Astronomy ch 3 pg 94

Question

An astronaut in space is floating 10 meters away from the command module, whose mass is 6000 kg. If the astronaut's mass is 80 kg, what is the gravitational force acting on the astronaut due to the module? What is the initial acceleration of the astronaut toward the module?

Answer 1

F = Gm₁m₂/r²

r = 10

m₁ (astronaut) = 80

m₂ (command module) = 6000

G = 6.67E-11 m³/s²/kg

Plug in the numbers to find the force (turns out to be 3.2E-7 N or, using appropriate sig figs, 3x10^-7 N)

To find the acceleration, use F = ma or a = F/m since we are talking about the acceleration of the astronaut, we use m = 80 so a = 3.2E-7/80 = 4x10^-9 m/s²

Make sense?