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So, with today's announcement, Opportunity was basically declared dead

When the dust storm originally engulfed Opportunity last year, mission scientists were hopeful that they might yet recover the rover. Sure, it had to steer with just two instead of four wheels, and the rover was showing its age. But even then, its batteries had retained 85 percent of their original capacity. Now, though, NASA scientists know it will never emerge from Perseverance Valley, a feature carved into the rim of Endeavor Crater by flowing water in a distant age.

Is there still a chance that some random wind or other event on Mars might clean Opportunity up and allow it to charge up again? And would it try to automatically phone home if it did?

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    $\begingroup$ Even if it did, either a relay on Mars orbit or the DSN network has to be trained on the signal at the right time. As these are limited resources, it would be highly unlikely anyone would be listening. $\endgroup$ – kert Feb 14 at 4:45
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The NASA announcement, available here, said specifically, "After more than a thousand commands to restore contact, engineers in the Space Flight Operations Facility at NASA's Jet Propulsion Laboratory (JPL) made their last attempt to revive Opportunity Tuesday, to no avail." [Emphasis mine]

They also said, "The final transmission, sent via the 70-meter Mars Station antenna at NASA's Goldstone Deep Space Complex in California, ended a multifaceted, eight-month recovery strategy in an attempt to compel the rover to communicate."

It costs a lot of money to have NASA Deep Space Network (DSN) stations or a Mars orbiting spacecraft track a lander or rover. As long as a project is officially active, there is money provided to keep up the tracking. But as soon as NASA declares "Mission ended" that money dries up, so there is no money to pay the people who would calculate when and where the DSN or Mars orbiter should point their antennas, or to pay the people on the lander project who negotiate antenna time with the DSN or a Mars orbiter project, or to pay for any of several other such activities needed to make such monitoring happen.

As @kert said, at this point even if something did happen to wake up Opportunity, it would be highly unlikely anyone would be listening. They'd have to be pointing an antenna at the right place at the right time, and would have to be listening to the right frequency band. Each spacecraft at Mars is assigned a narrow frequency band that is not shared with the other spacecraft at Mars, so you couldn't "accidentally" receive an Opportunity signal while listening to another spacecraft.

I expect that without solar power to operate internal heaters and with depleted batteries, getting very cold damaged one or more components like the batteries, interconnection cables, RF components, etc. Due to contrasts in thermal expansion coefficients, solder joints can pop, IC packages can break and connections pop, all sorts of things. Coming into winter, which starts later in 2019 for Opportunity's location, without pre-orienting to a survival position and attitude, at least some of those will probably happen, maybe even all of them.

This points out a couple of the advantages of a radioisotope power source (RPS), like the one on Curiosity (which is a radioisotope thermoelectric generator, RTG): the supply of electric power is independent of the amount of sunlight it is receiving; and the waste heat from the RPS is more than sufficient to keep the rover's insides warm, and if the thermal system is designed properly can keep the rover warm without requiring electronics to be operating. They just cost a lot!.

One quibble with the NASA announcement: there is no "70-meter Mars Station antenna" at a DSN station. The 70-meter antennas at the DSN stations are not dedicated to the Mars program. They are used for whichever project and spacecraft needs them, such as the two Voyager spacecraft. The 70-meter antennas are too valuable a resource to have any of them dedicated to a single project, especially if they would sit idle when Mars isn't in the sky above them.

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    $\begingroup$ re your quibble: Why does the word “Mars” shows up in google maps when viewing the Goldstone DSN complex? $\endgroup$ – uhoh Feb 14 at 6:03
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    $\begingroup$ @uhoh Yes, the antenna is called "Mars antenna", but there is no "Mars Station". But thanks for the link! $\endgroup$ – Tom Spilker Feb 14 at 6:46
  • $\begingroup$ Scott Manley had a comment in his video regarding RTG power sources. The rover was engineered to operate for three months. Solar power was better suited for such a short mission. The resulting fifteen years of operation was a spectacular return on investment, but not expected. $\endgroup$ – fred_dot_u Feb 14 at 11:21
  • $\begingroup$ Nice answer. Maybe you could also mention the cost of the support team necessary to operate the rover, in addition to the DSN $\endgroup$ – Antzi Feb 14 at 16:33
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    $\begingroup$ "Each spacecraft at Mars is assigned a narrow frequency band that is not shared with the other spacecraft at Mars". Well, that's supposed to be true. However MRO ended up with the same channels as Spirit to save a little bit of money on crystals, and since no one expected Spirit to survive as incredibly long as it would have to to still be alive when MRO arrived. Two years and two months? No way! So in fact, if somehow Spirit rose from the dead and started transmitting, you could in fact accidentally lock onto Spirit instead of MRO when trying to communicate with MRO. $\endgroup$ – Mark Adler Feb 15 at 3:56
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Is there any chance? Yes.

But, it's very, very, very, unlikely. There have been NASA missions which failed and disappeared only to mysteriously reawaken and continue to work. Most notably the IMAGE satellite broke and was abandoned until 13 years later a amateur found it transmitting. Opportunity is most likely permanently damaged and it's unclear what exactly happened, we can only guess from so far away. As far as we know the rover could still have power but be unresponsive due to damage to other systems.

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