Question

As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 25.2 km. You hold a hammer and a falcon feather at a height of 1.49 m, release them, and observe that they fall together to the surface in 28.8 s. Determine the mass of the planet.

Answer 1

circumference of the planet = 2r = 25.2 km = 25.2 x 1000 m

r = radius of planet

2 (3.14) r = 25200

r = 4012.74 m

distance travelled by hammer = d = 1.49 m

time taken = t = 28.8 sec

initial velocity = V_i = 0 m/s

using the kinematics equation ::

d = V_i t + (0.5)a t²

1.49 = 0 (28.8) + (0.5) a (28.8)²

a = 0.0036 m/s²

acceleration due to gravity is given as ::

a = GM/r²

M = mass of planet   , r = radius of planet = 4012.74 m , a = acceleration = 0.0036

inserting the values

0.0036 = (6.67 x 10^-11) M / (4012.74)²

M = 8.7 x 10¹⁴ kg