They work the same way radio wave transmissions work on Earth, only without an atmosphere they’re subject to a hell of a lot less interference (mostly due to atmosphereic ionization). Radio waves are on the electromagnetic spectrum, like visible light. As such, they move at the speed of light.
Radio waves, like light waves, move at (approximately, or “~”) 186,000 miles per second, or ~11,160,000 miles per minute. When we’re getting into distances that great, we often just convert them to light speed measurements. For example, ~186,000 miles is one light second, ~11,160,000 miles is a light minute, etc. A light year is ~5.878 *trillion* miles in case you’re curious.
So, to answer the question about how long it takes to send and receive signals, you have to know how far away things are. The moon, for example, is ~283,900 miles away from Earth, or a *touch* over 1.5 light seconds. There’s your answer. It takes a signal a *touch* over a second and a half to get from Earth to the moon, and any answer takes another second and a half to get back. Mars (right now, at least) is 106,973,891 miles away, or ~9.58 light minutes. It would take a transmission 9 minutes and 34(ish) seconds for a signal to get from Earth to Mars, and another 9 minutes and 34(ish) seconds to get a response.
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