On the way to the moon, the Apollo astronauts reach a point where the moon\'s gr

Question

On the way to the moon, the Apollo astronauts reach a point where the moon's gravitational pull is stronger than that of Earth's. Find the distance of this point from the center of the Earth. The masses of the Earth and the Moon are 5.98 x 10^24 kg and 7.36 x 10^22 kg, respectively, and the distance from the Earth to the Moon is 3.84 x 10^8 m. Answer in units of m. Also, What is the acceleration due to the Earth's gravity at this point? Answer in units of m/s^2. Universal gravitational constant is 6.672 x 10^-11 N*m^2/kg^2.

I got 34157300 m as my answer but that was wrong.

Explanation / Answer

GmMe/Re^2 = GmMm/Rm^2

Me/Re^2 = Mm/Rm^2

Rm/Re = (Mm/Me) = (7.36e22/5.98e24) = 0.11094

Re + Rm = 3.84e8

(0.11094+1) Re = 3.84e8

Re = 3.4565e8 3.46 x 10^8 m

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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