A question came up in the comments on the post Mars will pass behind sun, Rover operations affected, and the answer turns out to be very interesting.
The question was, to paraphrase, how often and when are the Earth based Mars rover operators out of radio contact with the Rovers? It turns out it is pretty complicated, so I'll reproduce the answer I got from Guy Webster, our man in NASA:
Opportunity (and Spirit when it's not hibernating), are out of contact most of the time every day. The rovers can communicate both directly with Earth and via relay through Mars Odyssey or Mars Reconnaissance Orbiter. On a typical day, a rover gets its commands for the whole day during a direct-from-Earth uplink for a few minutes in the Mars morning and sends home its report for the day via relay during a few minutes in the Mars afternoon, but commands have sometimes been sent via relay and downlinks have sometimes been sent direct-to-Earth (requiring more of the rover's energy expenditure per kilobit than doing it via relay). Timing for direct communications do depend on the rover's part of Mars facing toward Earth. For relays, the timing is related to the orbiter's passes in the sky over the rover, with some passes offering better geometry (for more data per pass) than others. The orbiters record the data, then transmit it home when they are in line-of-sight with Earth. The rover's part of Mars does not need to be facing Earth when the rover transmits to the orbiter.
...Bottom line is that the rovers do spend most of their time out of radio contact but that there are plenty of geometrically OK opportunities for communication.
Thanks Guy for that information.
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Interestingly, NASA is planing on putting a football field size antenna between Mars and Jupiter to act as a permanent relay between (possible future manned) Mars missions and Earth.
There is the further complication that when the SEP angle (Sun-Earth-Probe) becomes small enough, solar radiation begins feeding into the side lobes of the tracking station's antenna, raising the SNT (system noise temperature) and thus degrading the SNR (signal to noise ratio) of the ground receiver.
Mu, really? I tried Googling for that but found nothing. Got link?
There has been a "plan" for a deep space telecom relay for some years. I'm not sure it is an official mission. The idea is to lighten up the payload for deep space missions. Is this what you are talking about?
I think having a relay station just "somewhere" out in space (between Earth and the planet being observed) is not going to help. It is easier to erect a 100-meter dish on earth and pump megawatts into it than to send even something tiny into deep space (where the antenna diameter is limited to a few meters and power is hard to obtain).
The exception might be to have one big relay satellite very close to a swarm of probes, so that each probe needs only to cover the distance up to the relay. But even that is not trivially useful - around Jupiter, this small distance would be a few million kilometers, and after increasing the antenna diameter by a factor of 100 (i.e. Arecibo vs. relay), the same combination of power and antenna on the probe suffices for a few hundred million km, which is the distance between Jupiter and Earth.