An astronaut free falls toward the Earth at a distance of 3 Earth radii from the center of the Earth. What is his acceleration? Why is it 1.1 m/s squared?

a = 1.1 m/s^2

Explanation:

let a be the acceleration of the astronaut, M be the mass of the earth and r be the radius of the earth.

from the information provide:

the distance r is the radius of the earth.

the distance, d, the astronaut is from the surface of the earth and the only force acting on the astronaut is gravity, the astronaut accelerates with due to gravity only that is d = 3*r because we consider the earth center as the center of mass and gravity attracts object towards the center of mass.

then, we know that:

a = GM/d^2

= (6.67*10^-11) (5.972*10^24) / [ (3*6371*10^3) ^2]

= 1.1 m/s^2

Therefore, the Astronaut will be accelerating with an acceleration of 1.1 m/s^2 towards the earth.