Planet mass vs. orbital period

[Johnnyallen]

I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?

 

[jbriggs444]

I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?

If you equate the force of gravity, ##F=G\frac{m_{star}m_{planet}}{r^2}## with the force required to produce a circular orbit, ##F=m_{planet}\frac{v^2}{r}##, what happens to the mass of the planet?

 

[sophiecentaur]

I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?

The force attracting a planet depends on its mass but the effect of that force is divided by that mass so the orbit of planets is independent of their mass. However, if your planet's mass becomes significant, compared with the mass of the star it orbits, then star and planet will orbit around the centre of mass, which could be not near the centre of the star. See this link for some maths on the subject.

 

[DaveC426913]

If the mass of a body were a factor in its orbital velocity we could never have built the ISS.
Once it was larger than a single supply ship, we wouldn't be able to dock with it anymore!

 

[cjl]

If you equate the force of gravity, ##F=G\frac{m_{star}m_{planet}}{r^2}## with the force required to produce a circular orbit, ##F=m_{planet}\frac{v^2}{r}##, what happens to the mass of the planet?

To be fair, this is only true if M_star is much, much larger than M_planet. If the mass of the orbiting body and of the body being orbited are not dramatically different, then orbital period will absolutely depend on both masses.

 

[jbriggs444]

To be fair, this is only true if M_star is much, much larger than M_planet. If the mass of the orbiting body and of the body being orbited are not dramatically different, then orbital period will absolutely depend on both masses.

Right, as @sophiecentaur pointed out. This could be understood as the "r" in the gravitational force calculation not being the same as the "r" as in the distance to the center of mass of the two-body system.