Question

At what distance from the earth, on the line between earth and moon, an object will not feel gravity? Assume earth and moon as point masses and no other force by any other body. Earth=6*10^24kg

Moon=7.2*10^22kg

Distance=384000

Answer 1

Formula:

F = GMm/r^2

Data:

Mass of earth(Me) = 5.97E24 kg

Mass of moon(Mm) = 7.32E22 kg

Average distance between earth and moon(r) = 384400 km

Solution:

Let the point where the net force equals zero be 'x' km from earth, then,

G(Me)m/x^2 = G(Mm)m/(r-x)^2

=>Me/x^2 = Mm/(r-x)^2

=>(r-x)^2/x^2 = Mm/Me

Solving and substituting the data, we get

x = 346306 km

Hence, at 346306 km from earth, net force on a body due to earth's and moon's gravitational field equals 0