A spaceship is on a straight-line path between the Earth and the Moon. At what distance from Earth is the net gravitational pull on the probe from the Earth and the moon zero? Mass of Earth = 6×10^24 kg. Mass of Moon = 7×10^22 kg.

Question

Can someone please confirm if my answer of 4678km is right.

Answer 1

i got a similar answer
how did you work it out?

Answer 2

i used the centre of mass equation....

=(6x10^24*0)+(7x10^22*405608)/ 6x10^24+7x10^22

So how bout you? How'd you get to the answer?

Answer 3

i used both both masses and the distance to the moon

Answer 4

If the distance between the Earth and the moon is around 380,000km, doesn't 4,678km (assuming it is from the Earth) seem a bit too small? Earth is a much larger body than the moon, so the point where the gravity of the moon and the gravity of the Earth equal each-other (ie, cancel out) would be closer to the moon than to the Earth? I tried using GM(earth)M(spaceship)/r^2=GM(moon)M(spaceship)/(380000-r^2)
where G, and M(spaceship) cancel each other out so you can just solve for r, assuming it is the distance from Earth?