Two planets orbit a far away star as shown. is it possible that both planets experience the same gravitation force from the star? a) no, it is not possible. b) yes, it is possible if the closer planet has less mass. c) yes, it is possible if the closer planet as a smaller radius. d) yes, it is possible if the closer planet orbits the star in a shorter time.

As we know that gravitational force on two planets will be given as

let

mass of star = M

mass of two planets are m1 and m2

their distance from star is r1 and r2

since the gravitational force of star is given on two planets to be same

so here we can say

now if the ratio of mass and distance is same then we can say that closer planet must have lesser mass to hold good for above equation

so correct answer will be

B) Yes, it is possible if the closer planet has less mass.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west