How Do You Calculate the Mass of a Planet in Circular Orbit?

[DangoTango]

Homework Statement

A planet orbiting a star experiences a force of magnitude 3x1022N due to gravitational attraction to the star. If the planet has a speed of 2x107 m/s to complete on orbit, calculate the mass of the planet and radius of the orbit? Assume the orbit to be a perfect circle.

Homework Equations

I believe I have to use these equations but none of them really work for me at the moment.

I figured this would have something to do with it but I don't understand it.

The Attempt at a Solution

When I use any of the equations above I'm always missing something. These equations have been given by my teacher but at this point I'm not even sure I have the right equations. My attempt at a solution isn't even worth writing here. Please help!

 

[PeroK]

When I use any of the equations above I'm always missing something. These equations have been given by my teacher but at this point I'm not even sure I have the right equations. My attempt at a solution isn't even worth writing here. Please help!

It seems to me you need more information, like the mass of the star. What you have is correct, but only the ratio $\frac{m}{r}$ can be found,

 

[DangoTango]

It seems to me you need more information, like the mass of the star. What you have is correct, but only the ratio $\frac{m}{r}$ can be found,

Yeah that's what I was thinking bu thtis question was left as a challenge meaning that there must be something that can be done. I'd like to point out that it says the planet's orbit is a perfect circle.

 

[gneill]

That orbit speed, 2 x 10⁷ m/s seems awfully high to me. That's over 20,000 km/sec. For comparison Mercury's orbit speed is less that 50 km/sec, Earth's is around 30 km/sec. So, not a typical situation.

This planet couldn't orbit a typical star like our Sun (that orbit speed would imply an orbit well inside the Sun). So I'm thinking maybe you need to guess the nature of the star it orbits to deduce additional information?

 

[PeroK]

Yeah that's what I was thinking bu thtis question was left as a challenge meaning that there must be something that can be done. I'd like to point out that it says the planet's orbit is a perfect circle.

Why not take the planet's mass to be a) the Earth's mass; b) Mercury's mass and see what solutions you get for the star's mass, $M$, and the orbital radius, $r$?