This very nice NASA page continuously updates Voyager 1 & 2 distance away.
How is that distance calculated/determined?
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1$\begingroup$ By using Newtonian mechanics, our best knowledge of the distribution of stuff inside and near the solar system, and the measurements of the trajectory when it could still be detected. $\endgroup$– Andrew SteaneCommented Oct 5, 2020 at 22:44
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$\begingroup$ Thank you. So it is a “best guess” estimate. $\endgroup$– relayman357Commented Oct 5, 2020 at 23:28
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$\begingroup$ Best estimate is a better say to say it than best guess. One can calculate the trajectory one would see if the known matter was all there is. Deviations from that trajectory can be used to estimate where unknown matter is and how it is moving. That improves our knowledge of the matter out there. A calculation based on the improved knowledge gives a better estimate of the true trajectory. We can continue the calculation beyond where we can see the spacecraft. $\endgroup$– mmesser314Commented Oct 6, 2020 at 0:46
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3$\begingroup$ @AndrewSteane Not Newtonian mechanics. JPL uses a parameterized post-Newtonian (PPN) model of the solar system. In other words, it uses general relativity (better written: A somewhat simplified version of general relativity). $\endgroup$– David HammenCommented Oct 6, 2020 at 6:11
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1$\begingroup$ @relayman357 If you want to call estimates that are accurate to parts per billion, if not parts per trillion, yes, you can call those "best guess" estimates. But that is a bit disparaging. $\endgroup$– David HammenCommented Oct 6, 2020 at 6:18
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There is an article here that explains it where the normal "velocity $\times$ time" (velocity here is the speed of light which is multiplied by the time taken for the pulse to travel from the earth to the craft) calculations of distance are used but with more technicality. This is a snippet:
"Voyager 1’s communication system has a high gain parabolic dish of 3.7 meters in diameter to communicate with Earth. They use S-band for uplink and X-band for downlink. So to determine the distance of the spacecraft from Earth, they add a ranging pulse to the uplink and they transmit it to the spacecraft. When the Voyager receives this pulse, it sends it back to Earth. The time taken for the whole transmission and reception is recorded. As the electrical systems and computers take some time to process the signal in the Voyager, proper corrections are done to the recorded time by comparing it with the pre-launch data at NASA. Currently, it takes approximately 18 hours for a transmission from Earth to reach Voyager 1. So when one does the distance calculation with the recorded time and the known speed of the transmission (speed of light), one could easily know the distance. As of June 10, 2015, 10:17 UTC the distance between Voyager 1 and Earth was 130.81103152 AU. When added one AU (approximate distance between Earth and Sun) to it, we would get the distance between Voyager 1 and the Sun, which was 131.64053152 AU at that time".
The same thing presumably would be done with the Voyager 2 spacecraft.
