Question

The largest asteroid, ceres, has a radius 0.073 times the radius of earth and a mass of 0.0002 earth masses. how much would a 72 kg astronaut weigh on ceres in pounds?

Answer 1

By definition, the weight of a human being on earth is given by the following expression:
 f = m * g
 Where,
 m = mass
 g = gravity.
 On the other hand, gravity is also defined as:
 g = G * M / R ^ 2
 Where,
 M: Mass of the earth.
 G: gravitational constant.
 R: Earth radio.
 Taking these definitions into account then:
 For Ceres:
 gc = G * Mc / (Rc) ^ 2
 Where,
 Mc = 0.0002 M
 Rc = 0.073R
 Rewriting:
 gc = G * (0.0002 M) / (0.073R ^ 2)
 gc = (0.0002 / 0.073 ^ 2) * (G * M / R ^ 2)
 gc = 0.0375g
 Then, the weight will be
 fc = m * gc.
 fc = m * (0.0375) * g.
 (0.0375) * m * g
 (0.0375) * (72) * (2.2) = 5.94lb
 answer:
 a 72 kg astronaut weigh on ceres in pounds is  5.94lb