Imagine two spherical planets fixed on the x-axis, one with mass M at the origin

Question

Imagine two spherical planets fixed on the x-axis, one with mass M at the origin, and the other with identical mass M at the position x = +d. (Assume that d is much greater than the radius of either planet.)

a. At what position along the x-axis between the two masses could you position yourself so that you could experience a net gravitational force of zero?

b. Now imagine a similar arrangement of two planets separated by distance d, but with a mass of 4M at the origin. (The planet at x = +d still has mass M.) Again, at what position along the x-axis between the two masses would you experience a net gravitational force of zero?

c. Again, imagine a simiar arrangement of two planets separated by distance d, but with a mass of 2M at origin. (The planet at x=+d still has Mass M.) Again at what position along the x-axis between the two masses would you experience a net gravitational force of zero?

Explanation / Answer

a) at x = a/2 you can say it from symetry

b) F is inversely proprtional to r^2

net force to be zer0,

(r1/r2)^2 = 4

r1/r2 = 2

so at ,

x = 2d/3 , net F =0

c) r1/r2 = 2^1/2

r1/ (r1+r2) = (2^1/2)/d;

so the distance r1is (2^1/2 x d) / 2^1/2 +1

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