# Jupiter orbiting time in Earth's orbit?

Imagine if Jupiter orbited the Sun at the Earth's orbital distance of 1AU.

Would a planet of this size orbiting the Sun take 1 Earth year (365 days) to complete an orbit, or would the size of Jupiter affect its rotation and orbit?

The period of the Keplerian orbit of an object of negligible mass about some massive object is $$P = 2\pi\sqrt{\frac{a^3}{GM}}$$ In the above, $a$ is the semimajor axis length, $G$ is the Newtonian gravitational constant, and $M$ is the mass of the central object. When the orbiting object has non-negligible mass $m$, the above expression needs to be modified to $$P = 2\pi\sqrt{\frac{a^3}{G(M+m)}}$$
• Just to put in some numbers, if I use the full equation for the period, I get the Earth's orbital time to be $P_{Earth} = 365.268\:\mathrm{days}$ whereas for Jupiter I get $P_{Jupiter} = 365.095\:\mathrm{days}$. This means Jupiter's mass does have a measurable difference in the length of the year if it orbited at $1\:AU$, albeit not a very practical difference. At worst, the system of leap days would change under such an orbit. – zephyr Aug 17 '16 at 14:00