# Two planets with the same orbital period [duplicate]

I have the following star system configuration:

All bodies always stay on one line.

Star is similar to sun by parameters.

"Green" planet is Earth-like exoplanet with 1 earth-year orbital period, same mass and radius as Earth. It placed in L1 position between star and "grey" planet. More than that, "green" planet is tidally-locked between star and "grey" planet.

"Grey" planet is rocky planet, what is larger than "green" planet. I'm not sure about real size of this planet, maybe half of Jupiter mass.

It's interesting to imagine sky on dark side of "green" planet. Because observer may see "eye" in the sky, created by shadow of "green" planet.

I was trying to recreate this system in Universe Sandbox 2, but seems, that mass of the planet doesn't affect orbital period. So if I change period manually, simulation just decrease distance between planet and star (semimajor axis distance). But as I understand from orbital speed formula masses of both bodies are important.

So, can "Grey" planet have same orbital period (1 year) or not?

Thanks a lot!

• In the usual case the mass of the satellite or planet is very very much smaller than the mass of the primary; in this situation the orbital speed is determined only by the radius of the orbit. – AlexP Sep 25 '18 at 11:39
• Both science-based and reality-check are tagged. Those seek different answers - perhaps just one is appropriate. – user535733 Sep 25 '18 at 11:50

By the third Kepler's law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

It follows that to have the same orbital period, two bodies need to have the same semi-major orbital axis.

Since this is not the case for your configuration, the answer is no, it is not possible.

Therefore it also follows that it's not possible that

All bodies always stay on one line

• Thank you for fast, short and understandable answer. I will try to imagine something more interesting and realistic) – Losfer Sep 25 '18 at 12:56
• @Losfer As AlexP pointed out, the reason Kepler's third law holds in our solar system is because of the massive differences in, well, masses. If you want something else, maybe check out reddit.com/r/askscience/comments/4wbtc6/… I can't state definitively, but it seems that a system of two massive bodies (something like a binary star system) could orbit around a barycenter and a much smaller body could sit in between (closer to the system center than either of the two massive bodies). I doubt this system is stable for "long" though. – ColonelPanic Sep 25 '18 at 13:21