Question

The first asteroid to be discovered is Ceres. It is the largest and most massive asteroid is our

solar system's asteroid belt, having an estimated mass of 3.0 x 1021 kg and an orbital speed
of 17900 m/s. Determine the amount of work done on it by the sun's gravity in one full
revolution.

Answer 1

Answer: 0 J

Step-by-step explanation:

Assuming the asteroid is moving with uniform circular motion around the Sun, it is attracted by the Sun's gravitational force which is directed towards the center (that is why it is called Centripetal Force
`F_(c)`).

In addition, Cere's velocity is tangential to the orbit, this means the velocity vector
`V` and the centripetal force vector ar perpendicular
`F_(c)` (the angle between them is
`90\°`).

So, the work
`W` done by the Sun's gravitational force on Cere's is:

`W=F_(c) cos \theta d` (1)

Since the velocity is defined as a relation between the traveled distance
`d` and time
`t`:

`V=(d)/(t)`

And, since the distance is directly proportional to the velocity, which means it is in the same direction as velocity. The distance vector is also perpendicular to the centripetal force.

Hence:

`W=F_(c) cos (90\°) d` (2)

Being
`cos (90\°)=0`

Finally:

`W=0 J` (3)