Greetings once more MHF!

I have a couple of questions related to gravity that I think I have worked out fully but need to make sure of.

On all questions $\displaystyle g=10m/s^2$

Q1):

What force does earths gravity exert on a 81-kg astronaut who is orbiting in a space station at a distance from thesurfaceof the earth equal to 2 earth radii? Show your calculations. Your answer must be in Newtons.

A1):

2 radii from the earth surface is equal to 3 radii from the center of the earth.

By the inverse square law the gravitational, the gravitational force at '3d' is $\displaystyle (1/3)^2=1/9$.

Therefore, if the astronaut weighs 81kg, he weighs $\displaystyle 81*10=810N$ at 'd'. So at '3d' he weighs $\displaystyle 810*1/9=90N$

Q2):

The astronaut from the last question was launched into space by a Saturn rocket.

The upward acceleration of a Saturn rocket shortly after blast-off is $\displaystyle 80 m/s^2$. When the Saturn rocket is accelerating, what is the apparent weight of the astronaut, that is, what does the astronaut experience as the weight of his body?Show your calculations. Your answer must be in Newtons.

A2):

If $\displaystyle g=10 m/s^2$ then $\displaystyle 80 m/s^2=8g$. Thus, the total force acting on the astronaut is $\displaystyle g+8g=9g$ and $\displaystyle 9g=90m/s^2$

Therefore, his apparent weight is 90*81=7290N.

Thank you!