Find the relation between the gravitational field on the surface of two planets `A` and `B` of masses `m_(A), m_(B)` and radii `R_(A)` and `R_(B), `respectively if a. they have equal mass. b. they have equal (uniform)density.
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Let `E_(A)` and `E_(B)` be the gravtational field intensities on the surface of planet `A` and `B`. Then `E_(A)=(GM_(A))/(R_(A)^(2))=(G4/3piR_(A)^(3)rho_(A))/(R_(A)^(2))=(4pi)/3rho_(A)R_(A)` similarly `E_(B)=(Gm_(B))/(R_(B)^(2))=(4G)/3 pirho_(B)R_(B)` a. for `m_(A)=m_(B), (E_(A))/(E_(B))=(R_(B)^(2))/(R_(A)^(2))` b. For `rho_(A)=rho_(B),(E_(A))/(E_(B))=(R_(A))/(R_(B))`
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