Question

The asteroid Ceres has a mass of 7 ✕ 1020 kg and a radius of 960 ✕ 103 m. (a) What is g on the surface of Ceres? Incorrect: Your answer is incorrect. m/s2 (b) How much would a 76-kg astronaut weigh on Ceres?

Answer 1

The mass of the asteroid is given by

$M=7\times 10^{20}~kg$
And the radius of the star is given by

  $R=960\times 10^{3}~m$

a)
And the surface gravity is given by

$g=\frac{GM}{R^2}$
So, putting the given values, we get
$g=\frac{6.67\times 10^{-11}\times 7\times 10^{20}}{(960\times 10^3)^2}$
$\Rightarrow g=0.0507~m/s^2$

b)
  The weight of the mass $m=76~kg$, is given by

$W=mg=76\times 0.0507~N$
  $\Rightarrow W=3.850~N$