Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is √(aGM/(7R)) then the value of 'a' is _______. [Given: The two planets are fixed in their position]
We have to find the point where the gravitational field must be zero. EG = 0 GM/x² = G (9M)/ (8R-x)² 1/x² = 9/ (8R-x)² 8R - x = 3x => x = 2R Potential at A (surface of first planet), VA = -GM/R - G (9M)/7R = -16GM/7R Potential at point x, Vx = -GM/x - G (9M)/ (8R-x) = -GM/2R - G (9M)/6R = -2GM/R ΔV = Vx -
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