Jupiter is three pixels wide: shooting the planets with a phone

The 5x telephoto looks like it was built for the job. Find the brightest dot of the evening, lock focus, shoot. What lands on the screen is a small white marble, blown out, smooth as glass. You have photographed Jupiter, technically speaking. None of the planet is in there: no belts, no moon shadows, not even the polar flattening that shows up in every Victorian sketch. Noise is innocent this time, and so is your city sky. One number is to blame, and it is worth facing straight away.

A planet is far smaller than it feels

The NASA fact sheets give the Moon a mean apparent diameter at opposition of 1896 arcseconds, a shade over half a degree. Jupiter, the giant of the family, manages 46.9 under the same conditions, swinging between 50.1 and 30.5 across the cycle of oppositions. Saturn runs from 14.5 to 19.9, with 18.8 as its opposition figure. Mars reaches 25.6 only when the encounter is one of the good ones, and spends most of its time at a third of that. Venus tops the table at 66.1, which it hits while it is a razor-thin crescent nearly lined up with the Sun.

Do the division and your lens stops looking like the problem: the largest planet fits inside the Moon forty times over. Saturn claws back a little through its rings, whose outer edge sits at roughly 2.25 planetary radii, so the whole system spans a bit over forty arcseconds on a good night. These are still sizes the naked eye would file under “star”.

Three pixels, and that is the lot

Now the scale of your sensor. A 12-megapixel file is 4032 pixels wide, which works out to 8.9 micrometres per pixel once you map it onto a full-frame footprint. At the centre of the frame, one pixel covers 206265 times that pitch divided by the equivalent focal length, and on a 120 mm equivalent telephoto that comes to 15.3 arcseconds per pixel.

The arithmetic finishes itself. Jupiter at its best takes up three pixels. Saturn’s disc barely clears one, its rings fall short of three. Mars, in the finest opposition you will ever see, gets a pixel and a half. The Moon, through the same lens, sprawls across a hundred and twenty, which is precisely why the Moon works on a phone while the planets stay dots. Shooting at full resolution doubles every figure and changes no verdict. Six pixels are still six pixels.

Light is not the missing ingredient. Scale is

Set aside everything deep sky taught you, just for one night. On a nebula the signal is thin and you win by accumulating: short frames, hundreds of them, stacked until the noise backs off. A planet plays a different sport altogether. It is in full sunlight, it is close, and in a telescope’s field it behaves like a street lamp. Exposures drop to fractions of a second, sensitivity goes back to base, noise stops being the main character of the evening. The enemy changes, and so does the craft.

The phone looks into the eyepiece

The only way to buy scale is to put optics in front of the phone that already have it. This is afocal shooting: telescope and eyepiece form an image at infinity, the phone’s lens views it the way it would view a distant landscape, and the magnification is simply the telescope’s focal length divided by the eyepiece’s. A 1000 mm refractor with a 10 mm eyepiece gives you 100x. Your pixel scale divides by a hundred, from 15.3 arcseconds down to 0.15. Jupiter jumps from three pixels to over three hundred.

Before you go hunting for the shortest eyepiece in the catalogue, two brakes. The first is diffraction, which depends only on aperture and runs at roughly 1.22 times the wavelength divided by the diameter: at 550 nanometres, a 100 mm telescope separates detail about 1.4 arcseconds apart. That puts around thirty distinct details across Jupiter’s forty-seven arcseconds, and two pixels each is enough to record them. A disc a hundred pixels wide already holds everything the optics can deliver; pushing it to a thousand magnifies empty space. The second brake is the exit pupil, aperture divided by magnification, which has to fit inside the phone lens’s entrance pupil, a few millimetres across at best. Below about 20x the beam is too wide and the corners go dark.

Then comes the tedious part, the one that actually decides the night. The phone lens axis has to sit on the eyepiece axis within fractions of a millimetre, and stay there while the planet drifts across the field. Handheld, it is a lottery you lose most of the time. A rigid bracket with three independent adjustments is worth more here than any other piece of gear you own.

Air does more damage than a bright sky

Your 100 mm telescope promises 1.4 arcseconds of resolution. Whether you get them is the atmosphere’s call. ESO measures a median seeing of around 0.64 arcseconds at Paranal, one of the best sites on the planet, and counts as exceptional the sixteen per cent of nights that drop below half an arcsecond. That is the human race’s ceiling, achieved at 2600 metres in the Atacama. From your balcony, above roofs handing back the heat they soaked up all day, Jupiter boils like a coin at the bottom of a swimming pool.

Which is where the technique planetary imagers have used for twenty years comes in, and phones happen to be good at it: you record video. Sixty frames per second for two minutes gives you seven thousand images of the planet, each frozen in sixteen thousandths of a second, faster than the air can wobble. A few hundred of those frames caught the instant the column of air above you settled down. Software finds them, throws the rest away, stacks only the best. Lucky imaging is live stacking turned inside out: there you keep everything to gather light, here you bin ninety per cent to gather sharpness.

Two minutes, then Jupiter has turned

There is a clock nobody mentions. Jupiter spins once every 9.9 hours, the shortest day in the solar system. Over three minutes its surface travels 1.8 degrees of longitude, which at the centre of the disc amounts to three quarters of an arcsecond of apparent shift: under the seeing of a normal night, therefore invisible. Stretch to six minutes and the story changes, with the Great Red Spot smearing along its parallel. Two or three minutes of video is the honest ceiling for Jupiter. Saturn turns more slowly and shows less fine detail, so it forgives you; Mars, at a little over twenty-four hours per rotation, lets you take your time.

What you actually come home with

In order of rising difficulty. Jupiter’s two equatorial belts and the four Galilean moons come out of an 80 mm aperture on a mediocre night, and that is the result that recruits more people to planetary imaging than anything else. Saturn’s rings clear of the disc follow soon after; the Cassini division wants still air and at least 120 mm. The Martian polar cap appears only in the good oppositions, which come round every two years and two months and are not created equal. Venus offers a phase and nothing else, making it simultaneously the easiest target on the list and the dullest. Mercury, low on the horizon inside the worst of the atmosphere, belongs to people with a subscription to frustration.

The real leap is not optical, it is categorical. In the deep sky you fight darkness with patience; on the planets you fight air with speed. Same phone, same night, two jobs that resemble each other in nothing. And when the air shakes hard enough that stars dance to the naked eye, there is still a two-thousand-arcsecond target that could not care less: point at the Moon and save the evening.