A planet of mass 6 Times 1024 kg is at location m A star of

A planet of mass 6 Times 10^24 kg is at location m. A star of mass 8 Times 10^30 kg is at location m. What is the force exerted on the planet by the star? (It will probably be helpful to draw a diagram, including the relevant vectors.) F _on planet -

Solution

force between two masses is atrractive.

so force on planet by star will be towards star.

so first find displacement vector of planet to star , r

then r = r_star - r_planet

r = (7e11i, -4e11, 0)m - (-4e11, 7e11, 0) = (11e11, -11e11, 0)m

magnitude of r = |r| = sqrt(11^2 + 11^2) x 10^11 m

|r| = 15.56 x 10^11 m

r_cap = r /|r|

Force = GMm/|r|^2 ( r / |r|) = GMm r / |r|^3

F = [(6.67 x 10^-11 x 6 x 10^24 x 8 x 10^30 ) / (15.56 x 10^11)^3 ] (11e11, -11e11, 0)

= (9.35 x 10^20, - 9.35 x 10^20, 0 ) N