# Earth orbiting around sun - finding speed with known mass and radius

Hi,

the problem is stated as following:
The earth (mass=5.98×1024 kg) rotates around the sun in an orbit that is approximately circular, with a radius of 1.5×1011 m. Find the orbital speed of the earth around the sun.

[itеx]F=mv/r2[/itеx]

I get that I need to use this equation but I'm struggling with finding centripetal force. I understand it is equal to the force sun exerts on Earth and I solved the problem using equation [itеx]G\frac{mM}{r2}=\frac{mv2}{r}[/itеx] but I don't think it is the right solution according to the book since no information which is needed for this equation such as mass of sun (M) or gravitational constant (G) and we also haven't learnt this equation yet.

So how can I find centripetal force without using the force sun exerts on Earth? Or do I even need to use the equation for force mentioned above?

Thank you for any advice

## Answers and Replies

Doc Al
Mentor
Assuming the question is to find the orbital speed: How long does it take the earth to make one trip around the sun?

phyzguy
Science Advisor
If the radius of the Earth's orbit is 1.5x10^11 m, how far does it travel in completing one orbit? How long does this take?

Ok, I get it now, I just divide circumference (2∏r) by period (365 days, just in seconds).

Thank you both)

Yes, that is the easier way to do it.