Solve This Physics Problem

Question

If a planet with 7.7 times the mass of Earth was traveling in Earth's orbit, what would its period be (in years)?

Answer 1

Hello Elle B.,

Although technically the orbit of your new planet would revolve around the center of mass of the planet and the Sun (as does the Earth!), because the Sun is so massive the difference in orbital calculation is negligible. It would behave about like the Earth, period = 1 year by definition.

If you indeed want to (or are mandated to!) calculate exact corrections for sun/planet periods, you probably know enough to calculate the position of the center of combined mass? That gives a slightly altered (decreased) orbital radius, and the rest follows from Kepler's law T^2/r^3 = constant .

That means that any junk in space boosted out to fly in the orbital path of the Earth, has the same period. That does NOT mean that it is long-term stable, however. There are various points, called Lagrange points, that capture debris and hold it there, long-term stable (meaning, not perturbed by the Earth into flying away from those points). L4 and L5 are 60 degrees (pi/3) ahead and behind the Earth in its orbital path, the other three are on the Earth-Sun line. Look 'em up if that intrigues you.

-- Cheers, --Mr. d.