Let's say that these aliens have recently sent up a manned satellite into their orbit. Let's say these aliens mainly speak through sign language. How will these alien astronauts communicate with those down on the surface?
The same way we are doing right now.
We humans technically communicate by sound and body language. In practice, though, many people communicate more by text and emojis than by voice nowadays.
If the aliens are smart enough to put stuff in orbit, they should be able to read, type, and select different kinds of reactions for every message they receive on whatever IM app they are using right now.
In recent years people who use sign language have invented thier own writing system called signwriting. It is a written system of annotating sign gestures instead of phonemes which makes learning to read and write much easier for people who can not hear to be able to correlate sounds with a Phoenician based alphabet. Instead, all of the characters are meant to represent what you do with your body to sign. This way, a child who knows a sign language such as ASL can make informed guesses about how to read and write with the words they already know.
I don't believe a standardized signwriting keyboard exists yet, but presumably, you could develop a system that divides each gesture into somatic components such as facial expression hand actions, directions, transitions, etc. such that typing a series of keystrokes could be used to compile a full body gesture.
Once you establish a system of compiling words from thier simpler components, you can encode these components into a character set and store/send/receive writing just as efficiently as we can with English.
That said, broadcast TV was invented in 1928 before the space race began; so, your people will probably be able to radio broadcast video for expressing sign language even if they don't have a convenient system of converting written language into a digitalized written system yet. Recording it though would not be cheap. In 1961 when Yuri became the first man in space, video tapes costed about 3000 dollars per hour of film (when adjusted for inflation); so, there would be good reason to develop a written system in lue of just recording everything. Storing written language is about 2.25 million times more efficient than an uncompressed 640x360 RGB 30 fps video without an audio track. Even with modern digital computerized compression techniques, text is still on average 40,000 times as efficient; so, text is still often considered the preffered way of archiving and transmitting large amounts of information.
Assuming a visual feed of some kind if available, use that. If not, use a Morse-Code equivalent to represent the correct signs. If it's letter-based, i.e. the sign alphabet, this will be relatively simple; if it's not based on letter but rather uses unique signs for every word, this will be very difficult and thus worth looking into a constructed language of some kind to solve.
Right now the only thing we have in real-life that handles this is humans using sign language. I think this is the wrong model, because the idea is that an entire species is using sign language.
I can only guess at some of the evolutionary traits that make sign language better for these beings than voice. However, I'd like to state that sign language has some serious deficiencies when compared with simple vocal communication (yells, howls, and screams). For one thing, sign language is a short-range communication. It doesn't cover the case where somebody screams for help from a distance away. It might not even cover the case where somebody yells "Duck!" to get people to drop to the ground. For some things being deaf is worse than being blind.
Why would these beings using sign language rather than voice, and how could this be made more advantageous?
My suggestion is that these beings have at least a minimum hearing/vocalization organs for emergencies. Perhaps they have little control over the range of noises they can make, but they can use this to get others' attention.
One thing I suggest is that they have more dispersed eyesight than humans. Perhaps they have more than two eye-stalks. This would be useful when in conversation with another being and still continuing with whatever they are doing (typing, driving, etc.) They would also need at least two hands, perhaps more, for conversing.
As they raise in technology, they would develop some form of writing, to pass on information, or to communicate over long distances. This could become, as it has here on Earth, a form of electric/electronic communication. Eventually they would have computers, and need to communicate with them.
So I see that the alien station-keepers would use typing, and orbit-to-planet email. Eventually, they would have the technology and bandwidth to communicate visually, and use that for communication. They'd probably develop their own TentacleTube for sharing visuals to all other such beings.
Working with the premise of someone in orbit communicating in real time with someone on the ground, then they can't reasonably be sending physical written communications back and forth. However for a species to advance to the point of putting someone in orbit, they almost certainly need to have a writing system established (that's a huge part of what allows education and building on the discoveries of ancestors).
But then the existence of written language brings up an important point - someone had to develop a convention to express concepts as patterns of physical marks, which aren't the same as their normal sign-language. Whether you say it's based on individual symbols representing whole concepts/words (pictographs and such) or by multiple symbols being put together to have meaning (an alphabet of some sort), something of that nature would exist.
Once that idea exists, it's not a stretch for them to invent other conventions to convey concepts/words/language using other mediums than physical marks.
On way would be using very simple radio technology, one can send pulses of different lengths and thus have an equivalent of Morse Code. But if they have put someone in orbit, then they can presumably do more than just that with radio. Different frequencies and amplitudes can be used to encode information much more densely than Morse Code.
But what exactly might it be like, well that depends.
I presume they don't have a biology of effectively making sounds, but can they still hear? Then radio waves being heard by the receiving person as beeps or some other easily distinguishable sounds is a reasonable idea.
What if they don't have hearing? Then perhaps they decode the signals as blinking lights. Morse Code could work just as well if a person watches a light on their receiving device. Or if one presumes something a bit more sophisticated, then it could be an array of colored lights or perhaps a grid of lights (2x2, 3x3, etc) where each light responds to a different frequency/amplitude in the radio waves and then the receiving person interprets those patterns according to the established convention.
How about with a pantograph over a radio link.
A pantograph is a device to transfer a mechanical motion from point A to point B. One classic use is for a mass-signing machine. (Sign one document, make 100 copies of your signature.)
They can then be built powered and electronically controlled. We call this a "waldo" or "remote manipulator".
So, your aliens could develop a waldo system where one person wears something akin to gloves and a phone line equivalent transfers their motion to a remote viewer. The remote end would probably have mock hands (or other manipulative organ) with a arm-like sleeves over the works.
Once this telephone-analog is achieved, probably well before space flight, one need only change it to use a radio link to make it space viable.
The orbiting satellite can use a mirror to reflect sunlight down to the surface. Without a writing system, they must have tremendous memorization ability and the ability to detect fast movement. Otherwise, the amount of information needed to transmit technical information would take too long. Therefore, a mirror (or a set of mirror) would answer the question as posed.
The short answer is that their communication would depend substantially on their writing scheme. Like in our technology, the written message is transmitted first, because it is far easier to transmit than anything analog like spoken language.
The more interesting longer question involves the nature of their language. Sign language is not just a series of concrete signs. It conveys a great deal of emotive content in how you present the signs. Many who know sign languages lament how hard it is to convey what they really want to say in English because it lacks the subtle nuances they are used to having in their gestures.
So the fun question is what sort of a society might be built up around such a nuanced language. How might they differ from us? The answers to that question would materially affect the nature of their written language, and thus their communications here.