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physhelp · Feb 11, 2007, 06:55 PM

The earth has a mass of 5.97x10^-11kg. Sun has a mass of 2.0x10^-30. They are 93,000,000 miles apart. How fast does earth have to move to stay in orbit aroun sun?
How do you solve this?

Capuchin · Feb 11, 2007, 11:30 PM

For this question we assume that the Sun is so much bigger than the Earth that there is no movement of the Sun due to the movement of the Earth (unrealistic but a fair approximation). We also assume a circular orbit.

You have an equation for the gravitational force of the sun acting on the Earth:

$F = \frac{GmM}{r^2}$

Where G is the gravitational constant, m and M are the small and big masses (Earth and Sun) and r is the radius of orbit.

You also have an equation for the centripetal force required to keep a body in circular motion:

$F = \frac{mv^2}{r}$

Now, making them both equal we see:

$\frac{GmM}{r^2} = \frac{mv^2}{r}$

Cancelling:

$\frac{GM}{r} = v^2$

Now you need to put in your values for M and r (remember to convert to meters first) to get v, the orbital velocity

I don't know why your teacher gave you the mass of the Earth, it isn't needed.

Hope this helps :)

Capuchin · Feb 12, 2007, 11:18 PM

She?! ;)