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 25.3 km. You hold a hammer and a falcon feather at a height of 1.30 m, release them, and observe that they fall together to the surface in 29.1 s. Determine the mass of the planet.

Answer 1

circumference = 25.3 km

2*pi*R = 25.3 km

R = 4.03 km

s = ut +1/2 a*t²  for falcon feather or hammer

s = 1.30 m , u = 0 , t = 29.1 sec

1.30 = 0.5*a*29.1*29.1

a = 3.07 *10^-3 m/sec²

which is equal to = Gm/R²

Gm/R² = 3.07*10^-3

m = 3.07*10^-3 *4.03*4.03*10⁶ / 6.67*10^-11 = 7.47 *10¹⁴ kg