JUNO to Jupiter

Lets hope for some great photos and some interesting readings, after Juno's fly-by some 4,500 km above the clouds of Jupiter yesterday.

Will be keeping a special eye on the NASA website over the coming days.

Some lovely images from Juno:



Juno captured the Jovian rings from inside, anyone spot Orion??

Last week, NASA software engineer Kevin Kyle uploaded this picture of the shadow of Io on Jupiter, from Juno's flyby of perijove 22:



The crispness of the umbra is due to the Sun appearing five times smaller from Jupiter than from Earth, so it casts sharper shadows. But the shadow looks very big compared to Io transits pictured from Earth or like this one from the Hubble Space Telescope:



The lunatic fringe who believe all NASA photos are faked sometimes cite pictures of Earth as evidence, in which the the continents appear different and inconsistent sizes. I thought the Juno picture of Io's sharp shadow would give a way of demonstrating what's going on numerically. First we figure out how big the shadow would look from very far away where we can see an entire hemisphere of the planet. This is simple geometry:



By filling in the radii of the Sun, Io, and Jupiter, and the distances separating them, we can calculate the slope of the line, and thus the size of the umbra that Io casts on Jupiter. I find the ratio of Jupiter's diameter to umbra size to be 46:1. It seems reasonable when compared against the Hubble image for a sanity check.

Then we consider how things look for an observer who is a height h above a planet:



d is the distance to the observer's horizon, and r is the radius of the visible disc. This is obviously smaller than the full hemisphere radius R, so objects in images taken from far away will be smaller by a factor .

The triangle with sides r, d, and h, and the one with sides R, d and R+h are similar. Therefore:



By Pythagoras theorem we also have:



Thus:



... and this can be rearranged to:



So then I just measured the Juno image in a crappy drawing program:



and found the ratio of Jupiter's diameter to Io's shadow to be 6.6. This meant that:



... and:



Given the rough and ready nature, this compares well to Juno's height of approximately 8,000 km given in the NASA credit for the image. All's well with the world ... and Jupiter (but not with the lunatic fringe :pac: ).

The grooved terrain is fascinating. The relative lack of craters also indicates a young surface of ice.