Question

A space traveller weighs 540 N on earth. What will the traveller weigh on another planet whose radius is three times that of earth and whose mass is thirty times that of earth?

Answer 1

Given

space traveller weighs W_e = 540 N on earth
we know that the average value of g on Earth is g = 9.8 m/s2

so the mass of the space traveler is m = w/g = 540/9.8 kg = 55.102 kg

we know that the relation between g,G is, g = G*M/R^2

given let M1,R1 is regarding Earth and M2,R2 is another planet mass and radius

   R2 = 3*R1
   M2 = 30*M1

   so the ratio of the acceleration due to gravity is

   g2/g1 = ((30*M1)/(3*R1)^2)/(M1/R1^2) = 30/9 = 3.33

   g2 = 3.33*g1

   g2 = 3.33*9.8 m/s2

   g2 = 32.634 m/s2

now the weight of the space traveler on the another planet is W = m*g2 = 55.102*32.634 N

   W_p = 1798.198668 N

the traveler will weigh on the another planet is W_p = 1798.199 N