The Moon orbits the Earth once every 27.3 days. Suppose that a crazy billionaire

Question

The Moon orbits the Earth once every 27.3 days. Suppose that a crazy billionaire puts a satellite into orbit around the Earth, so that the satellite completes exactly 1.5 orbits of the Earth during every 1 orbit of the Moon. (Assume that both orbits are circular.) Calculate the ratio of the orbital radii of the satellite and the Moon. Which one is closer to Earth? Show your work completely. Express your final answer to 3 significant figures. Calculate the ratio of the orbital speeds of the satellite and the Moon. Which one moves faster? Show your work completely. Express your final answer to 3 significant figures.

Explanation / Answer

here ,

time period of new satellite , 1.5 * Ts = Tm , time period of moon

a)

Time period , T = 2*pi*sqrt(R^3/GM)

R= cuberoot( T^2*G*M /4pi^2)

then ,

the ratio of the orbital radii of satellite and the moon , ratio = cuberoot( Ts^2*G*M /4pi^2) /cuberoot( Tm^2*G*M /4pi^2)

ratio = cuberoot(1/1.5^2 )

ratio = 0.76

b.

v = sqrt(G*m /R)

the ratio of the orbital speeds of satellite and moon, ratio = sqrt(G*m/Rn) / sqrt(G*m/Rm)

ratio = sqrt(Rm/Rn)

ratio = sqrt(1/0.76)

ratio = 1.15

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.