NASA is putting pause on sending commands to its Mars exploration instruments from November 11 through November 25 as it waits out the Mars solar conjunction. With the sun in the way, any commands sent to Mars could suffer interference capable of harming the robotic explorers.
Can we? Yes. Should we do it right now? That's debatable.
The question is how much this would cost vs getting a two weeks offline every 26 months?
These two weeks do not create any additional requirements (you already have to make sure the probes can survive for a few weeks without comms), science does not fully stops during these two weeks. And it gives an opportunity to do long duration maintenance on the ground segment.
Frankly, there is little need to spend >$100M for such relays satellites until we actually have a permanent human presence on Mars.
Even when we have a permanent human presence on Mars, there isn't a great necessity to maintain contact for those two weeks. Even if something goes wrong, it's not like anyone could send help. Essentially it would be just so we knew what was going on, but that's not really a full time requirement.
The problem you face with that idea is that the satellites will have to have enough power to retransmit signals.
While the Mars > L3/L4 > Earth route is not much of an issue as the large receivers on earth can deal with a small power output at Lagrange. A signal moving in the other direction will have to be quite powerful to reach the small receivers on the Mars end.
Did you mean L5? L3 is always in line with the sun, so it doesn't seem like it would be useful for communication.
A signal moving in the other direction will have to be quite powerful to reach the small receivers on the Mars end.
Would it be easier to have a separate satellite for each direction, one at the Earth-Sun L4 point, and one at the Mars-Sun L4 point? Could we get a large enough dish to the Earth-Sun L4 point?
Alternatively, could we use lasers instead of radio? The SpaceX Starlink satellites have laser inter-links, and NASA just sent up the ILLUMA-T payload to the ISS last week.
We use very large radio dishes to communicate with craft at Mars, so that the spacecraft can use smaller dishes and less power. In order to add a relay at L4/L5, that relay would also need very large dishes and high power usage to reach the craft at Mars. Probably larger than anything we have in earth orbit today.
Is this a reference to young lovers of Victorian England communicating via encrypted messages via the personal columns in newspapers?
These “agony columns,” as they became known, provoked the curiosity of cryptanalysts, who would scan the notes and try to decipher their titillating contents. Charles Babbage is known to have indulged in this activity, along with his friends Sir Charles Wheatstone and Baron Lyon Playfair, who together were responsible for developing the deft Playfair cipher (described in Appendix E).
On one occasion, Wheatstone deciphered a note in The Times from an Oxford student, suggesting to his true love that they elope. A few days later, Wheatstone inserted his own message, encrypted in the same cipher, advising the couple against this rebellious and rash action. Shortly afterward there appeared a third message, this time unencrypted and from the lady in question: “Dear Charlie, Write no more. Our cipher is discovered.”