(1)
M=ρ*(4/3π*r^3)
F=GMm/r^2=Gρ*(4/3π*r^3)/r^2=4/3Gπmρr
ω=2π/T
F=mrω^2=mr*(2π/T)^2=4π^2*mr/T^2
4/3Gπmρr=4π^2*mr/T^2
ρT^2=3π/G
(2)
GMm/r^2=4π^2*mr/T^2
GM=4π^2*r^3/T^2
mgo=GMm/Ro^2
GM=go*Ro^2
go*Ro^2=4π^2*r^3/T^2
r=[go*Ro^2*T^2/(4π^2)]^(1/3)
GMm/r^2=mv^2/r
v^2=go*Ro^2/r
Er=0.5mv^2-GMm/r=0.5m*go*Ro^2/r-m*go*Ro^2/r=-0.5m*go*Ro^2/[go*Ro^2*T^2/(4π^2)]^(1/3)
(3)
W=Ep-Er=0-{-0.5m*go*Ro^2/[go*Ro^2*T^2/(4π^2)]^(1/3)}=0.5m*go*Ro^2/[go*Ro^2*T^2/(4π^2)]^(1/3)