gravity........physics help?

Question

To what height compared to earth can you jump on a planet with 4 times the radius of the Earth and a third of Earth’s average density?

If one day on this planet lasts 8 hours, how much lighter (in %) would you feel on its equator compared to the poles?

Finally, this planet is located at twice the distance as earth is from the sun, with its star eight times as massive as our sun. How long (in earth years) is one year on this planet?

Answer 1

Part 1
Let
V1 - Earth's volume
p1 - earth density them
mass of the Earth is m1= p1 V1
then
m1/m2=p1V1/(p2 V2)
V= 4/3 pi r^3
m1/m2 = (p1/p2)(r1/r2)^3
m1/m2=(3p1/p1)(r1/4r1)^3=
m1/m2=3 (.25)^3= 0.046875
so if you could jump on earth say 50cm
then on this planet you will not jump higher than
0.046875 (50 cm)= 2.34 cm


Part II
Centripetal acceleration is zero at the poles.

(g-a)/g

g=k M/R^2
a=V^2/R
V=2piR/(8 hours)

Part III
Work similarly as part I and part II
The gravity is balanced roughly by the centripetal force.
The rest is simple.