On what basis is the information about the distance and velocity of the Voyager probes determined?

Question

Voyager 1 was the first-ever object to reach interstellar space on August 25, 2012 when it passed beyond the sun’s realm of plasma influence (the heliosphere)[...] (source)

Although some of their instruments have been turned off to conserve power, we're currently still receiving data from the two Voyager probes, and will continue to do so for some time:

Even if science data won't likely be collected after 2025, engineering data could continue to be returned for several more years. The two Voyager spacecraft could remain in the range of the Deep Space Network through about 2036, depending on how much power the spacecraft still have to transmit a signal back to Earth. (source)

The JPL website offers information about the current distance and velocity of both probes:

Distance from Sun§: Voyager 1: 153.58332228 AU; Voyager 2: 127.70461507 AU

Velocity with respect to the Sun (estimated): Voyager 1: 38,026.77 mph; Voyager 2: 34,390.98 mph

§This is a real-time indicator of Voyagers' straight-line distance from the sun in astronomical units (AU). (source - my italics)

My question is:

On what basis is the information about the distance and velocity of the Voyager probes determined? Is this done by analysis of the data we receive from the probes? Or, are these values calculated based upon our current understanding of the way bodies move? Note that the distances above are shown as 'estimated' (but I'm unable to find information about the basis of that estimation).

My reason for asking this question is the (admittedly crazy) notion that we may be mistaken in assuming that interstellar space is fundamentally similar to the space surrounding a star. Is it possible that it actually isn't? We're learning new things all the time; take for instance the May 2021 news report about fluctuations in the interstellar medium, in which Jim Cordes, space physicist at Cornell, is quoted as saying:

“I have used the phrase ‘the quiescent interstellar medium’ – but you can find lots of places that are not particularly quiescent”

The Voyager probes are venturing into the unknown, and we currently -- for a limited period -- have a unique opportunity to test the hypothesis that interstellar space somehow differs from how we envisage it; but perhaps it won't be tested, if our belief in our current understanding of the 'laws' of motion is too strong.

I tried going to the horse's mouth to ask this question, but the contact page on the JPL website is 404 :(

Answer 1

On what basis is the information about the distance and velocity of the Voyager probes determined?

• For distance: round-trip travel time of radio signals
• For velocity: Doppler-shift of round-trip radio signals, and by the rate of increase in distance as discussed above.

The Voyagers as well as many other deep-space spacecraft before and after carry what's called a coherent transponder.

The simplest of these would be what's referred to as a "bent pipe"; a receiver that amplifies the radio signal and retransmits it exactly as it was received.

The problem here is that the received signal from so far away is incredibly weak and so the spacecraft can't transmit 5 or 10 watts at the exact frequency that it's also listening for $10^{-20}$ watts.

Phased locked loops to the rescue!

So instead the received signal is mixed with a local oscillator and heterodyne converted to a somewhat different frequency related by some rational number. From DESCANSO Chapter 3; Voyager Telecommunications

3.2.1.1 Uplink Carrier. Each Deep Space Station (DSS) transmits an uplink carrier frequency of 2114.676697 megahertz (MHz) to Voyager 1 and 2113.312500 MHz to Voyager 2. The carrier may be unmodulated or modulated with command (CMD) or ranging (RNG) data or both. Phase lock to the uplink carrier is provided. When the transponder receiver (RCVR) is phase locked, its voltage-controlled oscillator (VCO) provides a frequency reference to the exciter to generate a downlink carrier that is two-way coherent with the uplink.

The downlink frequencies are listed in Table 3.2:

             Coherent Downlink
              Frequency (MHz) 
Voyager 1       2296.481481 
Voyager 2       2295.000000
Voyager 1       8420.432097 
Voyager 2       8415.000000 

We can confirm that the ratios are rational fractions:

3.2.2.1 Downlink Carriers. When the transponder is set to the two-way coherent tracking mode and is locked to an uplink carrier, the received carrier frequency is used to generate phase and frequency coherent downlink carriers. The ratio between downlink frequency and uplink frequency is 240/221 for the S-band downlink and 880/221 for the X-band downlink.

For more on the technique of range-rate determination via delay-Doppler measurements check out various posts in Space Exploration SE tagged delay-doppler

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Effects of electrons from within the solar system and outside are small but they can not be ignored. They can be addressed by measuring the return signal at two different frequencies, since the small but measurable difference in the speed of a radio signal as a function of frequency is a simple function of electron density.

This is the same way that distances to fast radio bursts (FRBs) are determined.

From DESCANSO Series 1: Chapter 3; Range and Doppler Tracking Observables:

Tracking at a single-frequency band in the two-way mode has been assumed for each case. Dual-frequency downlinks, which are available from some space- craft, can be used to reduce the effects of the ionosphere and solar plasma. For example, solar plasma delays exceeding 200 m in S-band Viking Lander range measurements were calibrated to about 8-m accuracy using dual S and X down- links from the Viking orbiters [86,87]. Today, spacecraft operate primarily with an X-band uplink and downlink. Plasma effects for an X-band two-way link are reduced by a factor of 13 when compared to an S-band link. Future use of Ka-band two-way links would reduce this effect by an additional factor of 14.

For the current system, the random error of 0.03 mm/s for an X-band Doppler measurement made over 60 s is due primarily to fluctuations in solar plasma density along the line of sight. This value varies with proximity of the ray path to the Sun and with the solar cycle. The random error for a range measurement is due primarily to thermal noise.