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Would adding satellites along the path from Earth to Mars decrease the amount of time it takes to send and receive messages between them?

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No. Communication latency (the time between sending a bit and receiving it on the other end) between Earth and Mars probes is limited almost entirely by the speed of light, as they are radio waves on a direct path in vacuum. (There are also plans for optical communications, but as far as I know no Martian orbiter has yet been launched with that capacity. It wouldn't change the latency, though, as all EM waves of whatever frequency/wavelength travel at the speed of light in vacuum by definition.)

On the other hand, communication bandwidth, the amount of data transmitted per second, would probably increase significantly, since modern satellite communications are limited in bandwidth mostly by the fundamental limitations of signal-noise differentiation with a given transmitter power level, beam width, distance, and receiver size. So simply reducing the distance and using repeaters would greatly increase the bandwidth: every doubling of distance between links decreases the power loss to one quarter, and therefore improves the bandwidth by the corresponding four times or even better. You'd need some extra repeaters to compensate for smaller antennas and lower power budgets, however; as the largest dishes on Earth are around 70 m, and satellites' dishes have trouble reaching even a tenth of that, a back of the envelope calculation shows that you'd need at least ten intermediaries in sequence to match the current state of the art. Beyond that, every additional intermediate increases bandwidth, as long as they're distributed evenly. Since they would not likely be in a perfectly straight line, and because of the time for signal processing internally, latency would get slightly worse, probably a fraction of a second over the trip out of a total of 200–1200 seconds, which is pretty negligible.

Unfortunately, putting satellites between Earth and Mars isn't especially practical at the moment; intermediate orbits inevitably carry the satellites out of alignment, requiring either large solar sails to partially hover in place (and maneuver back and forth to a certain extent), or a large constellation of similar satellites (probably tens of thousands) to keep moving into position as each moves out of alignment. Solar sails have only been deployed a few times, and not for anything this adventurous, so this would require some new engineering work.

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  • $\begingroup$ And even if you place a constalation of satelite unless you are talking about thousands of satelites to avoid increace in latency in the closest aaproach and tens or hunds in the longest. That said it would probably be better to place a par of giant satelites to transmit between them. Swith to laser comunication migth improve bandwith as well. $\endgroup$ – OuNelson Mangela Oct 3 '17 at 7:54
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    $\begingroup$ I'm not so sure about bandwidth - satellite-to-Earth links can use a large dish on one end, satellite-to-satellite has only small antennas on both ends. A huge number of satellites, or laser communication would help though. $\endgroup$ – asdfex Oct 3 '17 at 9:02
  • $\begingroup$ @asdfex: Just having one or two intermediate satellites would not likely help much, no. But having quite a few would almost inevitably improve things. It's always the weakest link that governs bandwidth, obviously. $\endgroup$ – Nathan Tuggy Oct 3 '17 at 9:06
  • $\begingroup$ That's a lot of satellites, given that you need to replace one DSN 35m dish by dishes of maybe 4-8m you can fit on a satellite - maybe you can add some numbers to your answer. $\endgroup$ – asdfex Oct 3 '17 at 11:40
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    $\begingroup$ Very large (many tens of meters) lightweight deployable antennas can be used in space, whereas on Earth they would collapse under their own weight (or require much more extensive structure). e.g. the Orion SIGINT satellites have antennas of at least 100m diameter, larger than the largest deep space network antenna. $\endgroup$ – pericynthion Oct 3 '17 at 23:42
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Only for about two weeks every 26 months when Earth and Mars are in conjunction. The Sun blocks communications, so the latency is effectively that two weeks, or however many days remain. In that case a relay satellite in some intermediate orbit around the Sun not on that Earth-Sun-Mars line would reduce the effective latency.

Hardly seems worth the effort though. The conjunction problem could instead be greatly reduced or even eliminated much of the time with laser communications.

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