Question

Hannah has information about an object in circular orbit around Earth.

mEarth = 6.0 × 1024 kg

G = 6.67 × 10–11

What additional information does Hannah need in order to calculate the tangential speed of the orbiting object?

the mass of the orbiting object
the distance of the orbiting object to Earth
the orbital period of Earth
the radius of Earth

Answer 1

The distance of the orbiting object to Earth will give Hannah the radius which she needs.

Answer 2

The correct answer is:

the distance of the orbiting object to Earth.

In fact, we know that the gravitational force that keeps the object in circular motion around the Earth is equal to the centripetal force, so we can write:

`G(Mm)/(r^2)=m(v^2)/(r)`

If we re-arrange the equation, we find an expression for the tangential speed of the object:

`v=\sqrt{(GM)/(r)}`

and we see that it depends on 3 quantities: G, M (the mass of the Earth) and r (the distance of the object from the Earth).