How was the radius of Venus measured so accurately (± 3 km) via radar in the mid 1960's, before Venera 4 and Mariner 5?

Question

In several answers to the question When did planetary scientists realize Venus' surface pressure was almost 100x that on Earth? How did they find out? the known radius of Venus is mentioned.

It was necessary to have this when analyzing and interpreting the radio occultation data as Mariner 5 passed behind Venus (as "seen" from Earth). in order to associate each point in time with a distance between the radio path to the surface of the planet.

The two images below are from the report Mariner Venus 1967 NASA SP-190 (also here) and they show the radius (the horizontal line just above the x axis) to be:

6053 ± 3 km

Interestingly, in 2018, fifty years later Wikipedia gives a consistent and almost identical value, and after a half-century, the uncertainty has been reduced by only a factor of three!

6,051.8 ± 1.0 km

To get such a value, I'm guessing that the timing of radar signals from Earth was used, but analyzing the signal and extracting a distance with such a "small" (by 1960's standards) uncertainty (± 3 km) from a body that's ~12,000 km in diameter must have been a challenge.

The returned signal will contain power from all points on the planet's surface, with some obliquity and/or roughness factors and geometry worked in. It's not just a single "ping", but instead it's a hash of reflections with round-trip path lengths that might be spread out over as much as 12,000 km, geometrically at least.

However this is modified both by surface roughness distribution and strong refraction from Venus' very deep, very dense atmosphere.

And that means you need to do some modeling of the atmosphere (and perhaps surface roughness) to interpret the complex return signal in order to judge the distance to the planet's closest point, and the returned signal might be quite weak and noisy.

And even that just gives you the distance to the surface. To get a radius you need to know where the center of Venus is to kilometer accuracy (not just precision) relative to Earth, and I'm wondering if that requires some pretty meticulous orbital mechanics, astrometry, and understanding of the Sun's gravity field (monopole plus perhaps even its hefty J2?).

Question: How then was the radius of Venus measured so accurately (± 3 km) in the mid 1960's, before Venera 4 and Mariner 5?

Answer 1

In 1964, the Soviet scientist A.D. Kuzmin, together with the American scientist Barry Clark, began observing Venus using a movable radiointerferometer consisting of two 27-meter paraboloids (Owens Valley Radio Observatory, California). The radius of the hard sphere of Venus was measured: 6057 km (before that, astronomers measured only the radius of the cloud layer). Hence, the average height of clouds was also determined - from 40 to 60 km above the surface of the planet, which facilitated the subsequent calculation of the model of the atmosphere of Venus. Measurements of polarization of the radio emission of Venus showed that its source is a solid surface, not the atmosphere and not clouds, since only a smooth solid surface can produce radiation that is partially polarized at the edges of the planet's disk.

From book V.ALEKSEEV S.MINCHIN "Venus reveals secrets", Moscow, 1975 http://epizodsspace.airbase.ru/bibl/alekseev/v-r-t-75/01.html

Details about the experiment are described in the article by Kuzmin A.D. "Venus is a hot planet." Article on the official website of the Pushchino radioastronomy observatory. http://www.prao.ru/History/history_3.html

One of the first cooperation programs that was productive for both parties was the joint Soviet-American experiment Pushchino radioastronomy observatory and the US California Institute of Technology on determining the mechanism of Venus radio emission and its surface temperature proposed and implemented by A. Kuzmin. The Soviet-American agreement on scientific cooperation also included the exchange of scientists. In April 1964, A.D. Kuzmin was sent on a one-year business trip to the United States to conduct this experiment.

An experimental study of the presence of differential polarization was carried out on a radio interferometer at the Owens Valley Radio Observatory, California of the California Institute of Technology. The measurements were carried out from May 29 to July 18, 1964 near the lower junction of Venus, when the planet was closest to Earth and the intensity of the received radiation was highest, and the highest angular size of the planet also provided the highest spatial resolution. The work was carried out jointly with the young American scientist Barry Clark. The American side created the most favorable conditions for the work. The experiment was conducted as the most important work of the observatory. It is enough to note that 28 days of observations (!) Were provided, of which, not counting antenna swaps, adjustment and control measurements, 67 hours (!) were observations of Venus.

The measurement results found that the observed radio emission of Venus in the 10-cm wavelength range is polarized and, therefore, its source is the surface of the planet. The following physical characteristics of Venus were first determined by the intensity of radio emission, the polarization magnitude and the position of the zeros of the visibility function:

• The surface temperature of the planet is T = 700 ± 50 degrees Kelvin, i.e. above 400 degrees Celsius,

• radius of the body of the planet R = 6057 ± 55 km,

• atmospheric pressure at the surface P 80 ± 50 atm.

Two years later, the radius of the surface of the planet, determined with a higher accuracy on the radar of Venus R = 6056 ± 1 km, confirmed the results of radio astronomy measurements.

Six years later, the descent vehicles Venera-7 and -8 carried out direct measurements at the surface and determined a temperature of 740 K and a pressure of 90 atm, which also coincides with our data. But by this coincidence, there was still a long way to go of many events and heated discussions.

P.S.

For bigger informational content of an experiment, the configuration of the interferometer changed movement of the antennas installed on railway lines. At the end of every day of observations processing and the analysis of the obtained data was carried out and the decision on change of a configuration was made. In the morning of the next day antennas were transported on other planned stations. After each movement of antennas their adjustment was made. During the experiment was 7 such movements.

Answer 2

This was indeed quite a challenge.

The main advantage was having the mariner probe there. By determining the effect of Venus on the orbit of mariner, Having the exact distance to the surface of Venus using radar on-board Mariner and tracking data of Mariner itself allowed for a pretty good estimate.

In particular the difference in distance between where the CoM of Venus must be to effect Mariner in the observed way and the radar ping to the surface from Mariner gave the most reliable measure.

However as always, its a bit complex as you need a rough estimate of the atmosphere to have an idea of how much there is radar delay/scattering etc as you describe. This comes from telescope observations earth based radar etc.