The question
Printing the chart
You have the file. What do you actually do with it?
The download is a PNG at full print resolution, and that is the easy part. Choosing a size, a paper and a frame is where most people get it wrong, usually by letting a shop crop it.
What the file actually is
Every size is drawn from scratch at its final pixel count. Nothing is enlarged from the picture on your screen, which is why the star names stay crisp on a poster you could not fit through a doorway. A3 comes out at 3508 by 4961 pixels, A2 at 4961 by 7016, 18 by 24 inches at 5400 by 7200, and 24 by 36 inches at 7200 by 10800.
All four are 300 dpi, the figure printers ask for and almost never get. If your device cannot hold the largest canvas in memory — some phones cannot, and 24 by 36 inches is nearly 78 million pixels — the tool drops to the best resolution it can actually deliver and tells you what it did, rather than handing you a file that is quietly broken.
Which size, and a trap in the catalogues
The two inch sizes are exact. The two A sizes carry a rounding error of about three hundredths of a per cent against the true millimetre dimensions, which is far below anything a printer can hold and is mentioned here only because someone will measure it.
The trap is on the ordering side. Print shops tend to keep two separate product lines, one in centimetres and one in inches, and they do not always contain the sizes you would expect — a catalogue can offer a metric poster range with no true A3 in it, while the inch range has 18 by 24 and 24 by 36 sitting there. Check the actual dimensions in millimetres before ordering rather than trusting the name, because a poster sold as roughly A3 will leave you trimming or matting.
Paper
Matte, almost always. A star chart is mostly dark field with small bright points, and gloss turns every one of those points into a reflection that competes with the star next to it. Under a lamp a glossy print of a night sky is close to unreadable at an angle.
Weight matters more than people expect for something going behind glass. Anything under about 200 grams will ripple over time; 200 to 250 gram matte stock stays flat and is what most poster services use as standard. Heavier art papers look wonderful and are worth it for the larger sizes, where a thin sheet sags visibly.
The margin is already there
Every layout leaves a symmetric band of empty sheet above and below the chart — around a seventh of the height on A3, closer to a fifth on 24 by 36. That is deliberate. It is the room a frame needs, and it is why the type under the disc does not end up jammed against the mount.
Which means the one instruction worth giving a print shop is: do not crop, do not scale to fill, print at the size on the file. Borderless printing will eat the margin and, on the larger sizes, part of the lettering with it.
Where to have it printed
A local print shop is usually the best answer, and often the cheapest for a single copy. Take the PNG on a stick, ask for matte, and say the two sentences above about not cropping it.
If you would rather it arrived at your door, the sky tool shows a link to a print-on-demand service after you download. That link is an affiliate one and it is marked as such: if you use it, this site earns a commission, and if you print somewhere else the file is exactly the same file. Nothing about the download changes either way.