How Close Are These Two Planets?

−0

Using Kepler's third law, I get $$a=\sqrt[3]{\frac{P^2G\times(M+M)}{4\pi^2}}=5.32\times10^4\text{ kilometers}$$ where $a$ is the semi-major axis, $P$ is the time it takes the planets to orbit each other, $G$ is the universal gravitational constant, and $M$ is the mass of one of the planets - one Earth mass. The result is a semi-major axis of about 10 times the radius of Earth; the separation is twice this amount. I'd call this possible, though there would be very strong tidal effects.

Specifically, the tidal acceleration $a_t$ is treated as $$a_t\propto\frac{M}{D^3}$$ where $D$ is the separation, i.e. $2a$. The Earth is about 100 times the mass of the Moon, so that's an increase of about 100. Furthermore, the Moon orbits Earth at a distance of about 3.85$\times$10⁵ kilometers, about 3.85 times this separation. Therefore, we get an increase in tidal acceleration of about 5700.

That's a lot.

posted almost 8 years ago