One of the staples of SF art is images of alien worlds with satellites or planetary twins hanging low and huge in the daylight sky. This blog post brings he trope home by simulating what the Earth’s Moon would look like if it orbited the Earth at the distance of the International Space Station.
The author correctly notes that a Moon that close would play hell with the Earth’s tides. I can’t be the only SF fan who looks at images like that and thinks “But what about Roche’s limit”…in fact I know I’m not because Instapundit linked to it with the line “Calling Mr. Roche! Mr. Roche to the white courtesy phone!”
Roche’s limit is a constraint on how close a primary and satellite can be before the satellite is actually torn apart by tidal forces. The rigid-body version, applying to planets and moons but not rubble piles like comets, is
d = 1.26 * R1 * (d1 / d2)**(1/3)
where R1 is the radius of the primary (larger) body, d1 is its density, and d2 is the secondary’s density (derivation at Wikipedia).
And, in fact, the 254-mile orbit of the ISS is well inside the Roche limit for the Earth-moon system, which is 5932.5 miles.
The question for today is: just how large can your satellite loom in the sky before either your viewpoint planet or the satellite goes kablooie? To put it more precisely, what is the maximum angle a satellite can reasonably subtend?