# The asteroid Ceres has a mass of #7*10^20# #kg# and a radius of #500# #km#. What is #g# on the surface of Ceres? How much would a #99# #kg# astronaut weigh on Ceres?

##### 1 Answer

and the astronaut would *weigh*

#### Explanation:

To solve this question, we'll first need to understand how we can arrive at the value of

From Newton's Universal Law of Gravitation, we have:

Where,

and

(For a sphere, the centre of mass lies at its geometrical centre.)

But from Newton's Second Law, we have:

Substituting this in the first equation, we have

For a system consisting of an object on a planet or natural satellite,

and

*Since the radius of a planet is so huge, we can usually neglect small distances from it. The image looks more like this now:*

Alright, so we have reached on our final equation:

*It's interesting to notice that the value of #g# does not depend upon the mass of the smaller object #m#, which is why both heavy and small objects will accelerate towards a planet at equal rates. See Galileo's Leaning Tower of Pisa experiment .*

Now, substituting the values we have for Ceres, we get:

or,

Now for the second part, we know that the weight of an object

Substituting the values we have,

(You can compare this with

In case you want to know what a weighing scale from Earth would show in case the astronaut stepped on it on Ceres, you can divide his weight by

which is

**That's just what a weighing scale would show as we'd feel lighter on Ceres. The actual mass of the astronaut has not decreased!**