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
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