- #1

Vanessa Avila

- 94

- 1

## Homework Statement

A landing craft with mass 1.22×10^4 kg is in a circular orbit a distance 5.50×10^5 m above the surface of a planet. The period of the orbit is 5100 s . The astronauts in the lander measure the diameter of the planet to be 9.50×10^6 m . The lander sets down at the north pole of the planet.

What is the weight of an astronaut of mass 84.1 kg as he steps out onto the planet's surface?

## Homework Equations

circular motion speed: v = √GM/r

g: GM/r

^{2}

T = 2πr/v

## The Attempt at a Solution

I tried to solve for the speed by using the period.

5100 = 2π(5.50*10^5)/v

v = 677.6 m/s

and using the circular motion speed equation, I tried to solve for M, where the radius i used is the radius of the planet:

677.6 = √6.67*10^-11*M/4.75*10^6

M = 3.27*10^22

and then i used GM/r^2 to solve for G.

6.67*10^-11*3.27*10^22/(4.75*10^6) and i got a really small g. I think I'm missing something. Especially because I haven't used the space satellite's mass.