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The question Surface of Venus - what would it look like to see a spacecraft crushed by the atmospheric pressure? is a good one!

That plus comments below this answer got me thinking first about just how large the pressure is on the surface of Venus, and then "how did they first find out?"

Wikipedia states that Venus' atmospheric pressure at the surface is about 93 bar (93 times Earths' atmospheric pressure at sea level), which it says is like being roughly 900 meters below the surface of the ocean.

Very basic physics of atmospheres says that the pressure at a given height supports the weight of the atmosphere above it, and this gives an exponential behavior for a constant temperature, and can be calculated even for variable temperatures.

So what makes Venus' atmospheric pressure at the surface almost 100x larger than Earth's is (to 0th order) that there's almost 100x more of it. If you piled on 99 times more N2/O2 on Earth, then at least for a short while, the pressure here would be roughly like that of Venus.

Of course in reality its much more complicated.

So I'd like to ask what were the earliest observations that led to planetary scientists to know that the pressure was so huge; that it wasn't 2x or 5x or even 20x Earth's, but that it was almost 100x?

We can't see through the atmosphere in visible light, but that's so much material that the index of refraction would slow down precision interplanetary radar, so it's possible that careful timing of radar signals, along with a good ephemeris and understanding of Venus' period could detect it, but there were also some early spacecraft that may have sent telemetry, and those would have measurable ranges as well, so without a local altimeter, you still could know it's approximate distance from the surface.

These are all hypothetical, but I'm interested in the facts. When did scientists first realize that landers would need to withstand such pressures to survive there?

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The early Venera probe hulls were designed for an atmospheric pressure of 25 bar. Barometers were designed for 10 bar. This was in line with what was then assumed to be the surface conditions.

At the time, it was thought that the surface temperature of Venus was approximately 300C, with an atmosphere consisting mainly of carbon dioxide and nitrogen at about 20 bars. Consequently, the capsule was designed to survive 300C and 25 bars.

The capsule was also subjected to 500g acceleration tests.

There was a wide variety in surface pressure estimates, by the way.

In 1967, most astrophysicists in America and Russia believed that Venus was extremely hot, but one MIT paper that year suggested the planet could be experiencing an Ice Age! Surface pressure on Venus was even more of a scientific guessing game at that time, with published estimates ranging from 3 to 1000 atmospheres. This uncertainty resulted from the inaccuracy of spectrographic methods, which measured conditions at the cloud tops, and from uncertainty about the depth of the atmosphere and the radius of the planet's hard surface. Estimates of 10 to 30 atmospheres of pressure at the surface were commonly believed. The presence of carbon dioxide was obvious from infrared spectroscopy; and prior to Venera-4, a composition of 15% CO2 and 85% nitrogen was considered likely.

Venera 4 was the first to get usable data during the descent, it stopped transmitting when pressure hit 22 bar.

Mariner 5, whose mission coincided with Venera 4, found a surface pressure of 75-100 bar and temperatures around 500 ºC

On October 19, after a 127-day flight from Earth, Mariner 5 flew within 3,990 km of Venus, becoming only the second successful Venus exploration mission in history. The spacecraft provided detailed information about the planet’s atmospheric pressure (75-100 atmospheres) and temperature (527 ºC), and found no trapped radiation belts around Venus as its magnetic field was only 1% as strong as Earth’s.

This is how the final data was arrived at:

The precise radio tracking of the Mariner 5 spacecraft has enabled the distance from the center of Venus of the line-of-sight joining the tracking station and the spacecraft to be determined with an uncertainty of less than 0.2 km near the time of occultation. The resulting profiles of temperature and pressure, when superimposed on the data of Venera 4, indicate that the Soviet probe penetrated to a radial distance of about 6079 km from the center of mass of Venus. If this is assumed to be the radius of the solid surface of Venus, it is at variance with the results of earth-based planetary radar studies. Extrapolation to the radar radius leads to atmospheric models that are consistent with the results of passive radio astronomy. It is concluded that the Venera 4 probe either landed on a high plateau or surface feature undetected by radar, or did not continue its measurements to the surface of Venus.

The Mariner mission ran a radio occultation experiment to measure Venus' surface radius and get some atmospheric data.

By far the most interesting results came from the radio occultation observations which probed the atmosphere of Venus independently of Venera 4. Because of the density of the atmosphere, S-band transmissions could only probe down to a point 6,085 kilometers from the planet’s center or about 32 kilometers above the radius of Venus derived from Earth-based radar observations. At lower altitudes, the atmosphere becomes super-refractive and radio signals are bent around the planet. Extrapolating down to the surface, the temperature was expected to be between 377° C and 527° C with a pressure somewhere between 75 and 100 bars, depending on the assumptions made about how much carbon dioxide and nitrogen were in the atmosphere. These values were far in excess of what Venera 4 had recorded when it was allegedly near the surface of Venus. So what happened?

A reexamination of the measurements of Venera’s results showed that the radar altimeter data had been misinterpreted. Instead of transmitting data all the way to the surface, Venera 4 had actually stopped transmitting data at an altitude of 26 kilometers either because of structural failure caused by the higher-than-expected atmospheric pressure or the exhaustion of its battery (which was nominally rated at 100 minutes) by the longer-than-expected descent. While Venera 4 was the first Soviet spacecraft to reach another planet in operational condition, it was not the first spacecraft to transmit data from the surface of another planet. Although disappointing, the in situ measurements returned by Venera 4 were of immense value. Combining the data on the atmosphere and its composition as measured by Venera 4, by 1969 Soviet planetary scientists had extrapolated their data to show that the surface temperature as about 442° C with a pressure of 90 bars – very close to today’s accepted values and a bit closer to the mark than those of Mariner 5. The complementary data sets of Mariner 5 and Venera 4 had finally resolved one of the long standing mysteries of Venus.

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  • $\begingroup$ Mariner 5 was a flyby mission, not a lander. $\endgroup$ – Hobbes Aug 29 '18 at 8:30
  • $\begingroup$ Indeed it is! Figs. 5 & 7 (click "print this article" to view): adsabs.harvard.edu/full/1971AJ.....76..123F the plots clearly extrapolate to about 100 bar, QED ;-) or click PDF here: adsabs.harvard.edu/abs/1971AJ.....76..123F $\endgroup$ – uhoh Aug 29 '18 at 9:37
  • $\begingroup$ I've found some more sources as well. I don't want to post a new answer if you are still working on this, but if you feel you're mostly done, then I'll go for it. $\endgroup$ – uhoh Aug 29 '18 at 10:34
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    $\begingroup$ Go ahead, I'm done. $\endgroup$ – Hobbes Aug 29 '18 at 10:53
  • $\begingroup$ The data combination mentioned in your last paragraphs can be seen in the first plots of my answer. Thank you very much for your help! I'd like to think that getting to the bottom of this has been a real team effort! $\endgroup$ – uhoh Aug 29 '18 at 13:05
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The determination that Venus has a hellish surface is a great example of scientific detective work and its close association with technological advances that allow better and better measurements.

In 1952 Harold Urey had argued that with a roughly Earth-like atmospheric density (postulated, not measured!), its position orbiting ~0.72 AU from the sun should make its average surface temperature somewhere around 53 C (326 K, ~127 F) [H.C. Urey, On the Early Chemical History of the Earth and the Origin of Life, Proceedings of the Nat'l Academy of Sciences of the USA, Vol 38 #4, pp.351-363, Apr. 15 1952]. Others proposed even cooler temperatures. NASA's final report for the Mariner 2 mission to Venus (look out, that's 360 pages!) begins with a summary of what was known before the Mariner 2 mission's observations, stating "Observers have visualized Venus as anything from a wet steaming abode of Mesozoic-like creatures, such as were found on the Earth millions of years ago, to a dead, noxious, and Sunless world constantly ravaged by winds of incredible force."

The scientifically-based detective story begins in the 1950's with ground-based (Earth's ground, of course!) radio astronomical observations, where you point a big dish antenna at a planet and measure the intensity of the radio energy the planet is emitting. Often you measure not just at one frequency but at multiple frequencies, or a continuous range of frequencies, to get a radio spectrum. If you assume the body emitting the energy acts as a black body, then if you know the projected area of the body (as seen through the radio telescope) the intensity of that energy at a given frequency can be translated to the body's effective black-body temperature, called its brightness temperature. The process of translating measurements to inferences of other physical parameters is called data reduction, so in the literature you often see references to "measured fluxes reduced to brightness temperatures". If you have spectral data whose wavelength dependence is like a black-body spectrum, you can derive an effective temperature without knowing the body's projected area. In the 1950's antenna technology got to the point they could build parabolic reflectors for dish antennas big enough, and receivers could be sensitive enough, to detect radio emissions from the terrestrial planets. Nowadays we have antennas large enough, and interoferometric techniques sufficiently mature, that radio observatories can resolve planetary disks into many pixels, resolving spatial variabilities in the planets being observed, but back then you received radio emissions from the entire Earth-facing side of the planet all at once; one pixel.

This source provides an excellent summary of the early ground-based measurements and the puzzles they posed. Along with the Wikipedia article, they provide good general references for this question's topic, and most of the summary that follows.

Mayer, McCullough, and Sloanaker made the first successful radio astronomical observations of Venus in 1956; they published reports that year in the Proceedings of the IRE (Institute of Radio Engineers; this publication was subsumed into the Proceedings of the IEEE in 1962) but I can't find the paper itself online. In 1958 they published more extensive results, including radio fluxes at 3.15 cm wavelength reduced to blackbody temperatures around 600 K. In the appendix they report additional observations at 9.4 cm giving a temperature of 740 K, very near the current estimate for temperatures at Venus's lowlands, which constitute most of the planet.

This contrasted with the measurements at millimeter wavelengths by A.D. Kuzmin that showed brightness temperatures near 300K, and a spectrum that looked nothing like a black body. Scientists came up with two ways to produce this spectrum (two prime suspects! ;-): 1) the surface is hot, but at shorter wavelengths the atmosphere becomes opaque, so observations at those wavelengths are seeing radiation from higher in the atmosphere where it is cooler, not from the surface; 2) the surface is cool, but processes in the ionosphere radiate strongly in the cm-decimeter range of the radio spectrum, making it look hot at those wavelengths. Both of these models could fit the spectrum, so no reliable conclusion could be reached regarding which model was right (which suspect was the one we're after). Optical spectra had indicated the presence of $CO_2$, so in his 1960 doctoral dissertation Carl Sagan supported the hot-surface model, proposing that the $CO_2$ greenhouse effect could contribute to high temperatures in the lower atmosphere and at the surface. The one sticking point with the hot-surface model was that to get enough atmospheric opacity to make the short-wavelength observations 300 K cooler than the cm-wavelength observations required atmospheric pressures in the 20-100 atmospheres range. At the time scientists took the view that The pressure of such an Earth-like body can't be that high!...(...can it??...) so they didn't quickly adopt Carl's suggestion.

Ground-based radio astronomical measurements in 1962-1964 used new, larger dishes and new techniques such as interferometry that allowed higher spatial resolution. These lent some support to the hot-surface model when they detected limb darkening at Venus at ~3 cm wavelength (although that source refers to stars, the concept of limb darkening applies to planets and other bodies too). A month later the Mariner 2 spacecraft, using an instrument that was essentially a radio telescope, just placed a lot closer to Venus, also measured limb darkening at 1.9 cm wavelength. But a Caltech ground-based interferometer operating at 10 cm wavelength observed limb brightening, leaving the scientists scratching their heads and wondering What the...heck???

(Aside: about this time scientists began making radar observations of Venus, using the NASA Deep Space Network's largest antennas and the huge Arecibo facility (both a radio and a radar telescope). A radar telescope transmits a very strong signal to the target body, somewhat akin to illuminating an object with laser light, and then receives and records the reflected signal. Soon after, Stanford University built a dedicated radar telescope in the hills above the main campus. These radar systems were able to begin the mapping of surface features at Venus, and reliably measure for the first time Venus's rotation rate.)

Astronomical methods of the time had achieved all they could do regarding the problem, so this dichotomy of two competing models (two prime suspects) remained until we actually got there with better instruments and techniques.

After Mariner 2 scientists knew solving the puzzle would require new techniques and instruments. At Stanford, scientists and engineers had developed the radio occultation method (Prof. Von R. Eshleman was my Ph.D. advisor!) for measuring vertical profiles of atmospheric pressure and temperature. This technique involves flying a spacecraft behind the destination planet as seen from Earth. Just as a spacecraft is starting to go behind the planet ("immersion") or as it's coming out from behind the planet ("emersion"), the radio signals traveling between the spacecraft and Earth pass through the planet's atmosphere. Careful reduction of the phase, Doppler shift, and amplitude of the resulting signals provide these vertical profiles, and more. The same observations can characterize the electron densities in a planet's ionosphere, and detect radio-absorbing constituents in the neutral atmosphere.

Mariner 5 performed a radio occultation experiment at Venus. Preliminary results (abstract only, the full paper is behind a paywall; full reference is: Atmosphere of Venus as Studied with the Mariner 5 Dual Radio‐Frequency Occultation Experiment, G. Fjeldbo, V.R. Eshleman, Radio Science Vol. 4 #10 pp 879-897, October 1969 DOI: 10.1029/RS004i010p00879) concentrated on the ionospheric results, but did show that at ~35 km altitude the signals reached critical refraction. Critical refraction is where the refractive curving of the signals' ray paths is so large that any horizontally-traveling signal at a lower altitude has its radius of curvature smaller than the distance to the center of the planet, so the signal is effectively trapped within the atmosphere. So, unfortunately, the radio occultation method couldn't probe deeper than that. But what they did see from preliminary data reduction verified that temperatures were zooming with decreasing altitude, and the pressure at 35 km altitude was already high, nearly 10 atmospheres. This strongly argued for the hot-surface model.

In Oct. 1967 the Soviet Venera 4 used the atmospheric entry probe technique to directly measure atmospheric temperatures, pressures, and composition. It wasn't designed to handle pressures as high as it encountered so it made measurements only to 26 km altitude, but its results were consistent with the Mariner 5 radio occultation measurements: at 26 km altitude the temperature was 262 C (535 K) and the pressure 22 atmospheres. It also made the first direct measurements showing that Venus's atmosphere was overwhelmingly $CO_2$ with a few percent of $N_2$ and only traces of anything else, notably water. That much $CO_2$ makes for a powerful greenhouse effect. Atmospheric physics dictates that as you go lower in the troposphere it will only get hotter, and the pressure will only increase. Atmospheric models using the equations of atmospheric behavior were now predicting surface temperatures of 600-800 K and pressures of 90-100 atmospheres, and these were considered reliable: scientists then accepted that Venus's surface was a good model for Hades.

Those observations laid to rest the notion that the surface of Venus was like a very hot tropical jungle, i.e. the cool surface model. Hypothesis #1, the hot-surface model, was convicted. It was sentenced to be bandied about seemingly endlessly in professional journals, the popular media, etc.

(Historical note: At first the Venera 4 team claimed that they'd made measurements all the way to the surface, so the 262 C was a surface temperature. It didn't take long for scientists and engineers to figure out that the probe's radar altimeter had suffered from altitude aliasing, and its deepest measurements were actually from 26 km altitude.)

In 1971, armed with the Soviet Venera 4 results in addition to the Mariner 5 results, the Mariner 5 team published a more comprehensive paper. (Again, abstract only/paywall; full reference: The Neutral Atmosphere of Venus as Studied with the Mariner V Radio Occultation Experiments G. Fjeldbo, A. Kliore, V.R. Eshleman, Astronomical Journal Vol. 76 #2 March 1971 DOI: 10.1086/111096) At 35 km altitude the temperature was 500 K (227 C) and the pressure ~9 atmospheres. Extrapolating their profiles to the surface indicated a surface temperature of 775-800 K and a pressure of 90 atmospheres (~91 bars), though they noted that if the temperature lapse rate observed in the 50-35 km altitude region changed below 35 km the surface temperature could be different.

Indeed that lapse rate does change, and the current accepted values for the average temperature and pressure at Venus's lowlands are 735 K and 92 bars. But the measured temperatures and pressures above 35 km agree well with subsequent in situ and radio occultation measurements. The radio occultation measurements turned out to be very accurate.

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  • $\begingroup$ Wow! okay I'll give this a thorough read today, thank you! $\endgroup$ – uhoh Sep 3 '18 at 1:47
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    $\begingroup$ @uhoh There are some funny stories (and some interesting ones) about the Stanford radar system, not strictly appropriate for comments on questions or answers, but maybe a chat sometime... $\endgroup$ – Tom Spilker Sep 3 '18 at 2:00
  • $\begingroup$ ping me there any time! $\endgroup$ – uhoh Sep 3 '18 at 2:07
  • $\begingroup$ @uhoh OK, how do I start a chat? $\endgroup$ – Tom Spilker Sep 3 '18 at 2:55
  • $\begingroup$ Easiest way is to use the main chat room (scroll down to the bottom of the page and look for Chat), then select the room called The Pod Bay or just use this chat.stackexchange.com/rooms/9682/the-pod-bay Or after clicking Chat you can click "create a new room" $\endgroup$ – uhoh Sep 3 '18 at 3:04
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My 1965 Sourcebook on the Space Sciences describes three then-current models for the Venusian atmosphere: the greenhouse, aeolosphere, and ionosphere models. Without going into too much detail, the first two models expected to find roughly 5 atmospheres pressure at the surface, and the third model expected about 1 atmosphere. The book also mentions the flyby of the Mariner II spacecraft, which observed microwave "limb darkening" -- i.e. it detected more microwave emissions from the surface of Venus than from the atmosphere, which was consistent with the 5-atmosphere greenhouse and aeolosphere models but not with the ionosphere model.

Venera 4 failed at about 26 km altitude:

The capsule deployed its parachute at an altitude of about 52 kilometres (32 mi), and started sending data on pressure, temperature and gas composition back to Earth. The temperature control kept the inside of the capsule at −8 °C (18 °F). The temperature at 52 km was recorded as 33 °C (91 °F), and the pressure as less than 1 standard atmosphere (100 kPa). At the end of the 26-km descent [from the 52-km parachute deployment altitude], the temperature reached 262 °C (504 °F) and pressure increased to 22 standard atmospheres (2,200 kPa), and the signal transmission terminated.

Though it's at least as likely that the oven-broiler temperature killed the probe as the pressure.

The Wikipedia article on Venera 4 suggests that a denser atmosphere was expected by 1967:

the pressure readings by the capsule [22 atm at 26km altitude] were much lower than predicted by the recently-developed models of the Venus atmosphere [for the Venusian surface]

I haven't been able to find out anything about the development of atmosphere models between 1965 and 1967.

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  • $\begingroup$ Thanks! So for Venera 4 the 22 bar needs to be assigned an altitude before it can be used as an indicator of the potential surface pressure. While I mentioned planetary radar from Earth, it turns out Venera 4 had radar ranging capability, reading further in your link, there is quite an interesting situation with the interpretation of that data: en.wikipedia.org/wiki/Venera_4#Radar_Altimeter that might be of interest to readers. $\endgroup$ – uhoh Aug 29 '18 at 1:41
  • $\begingroup$ @hobbes' link explains further about this issue with Venera 4's radar. It looks like measurements of Venus' planetary diameter via radar from Earth was used to address this ambiguity. A re-read of my question will show I had a hunch Earth-based radar would have somehow been involved, though it looks like it was in a different way than I'd considered. If you can squeeze a bit of this in to your answer, I'll delete these comments. $\endgroup$ – uhoh Aug 29 '18 at 2:04
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This is what happened:

The report Mariner Venus 1967 NASA SP-190 (also here) says, and I am seriously shortening:

On the day before Mariner 5 encountered with Venus, the Soviet probe, Venera 4 dropped through the atmosphere on a parachute. […] Rough measurements of the atmospheric composition were made near the beginning of the descent… From these measurements, the Soviet scientists constructed an atmospheric model for a region in the atmosphere that they assumed (on the basis of a single radioaltimeter measurement) corresponded to altitudes from 0 to 26 km.

[…]Considering all information available, including the radar and radiometer results in the microwave region, the only tenable assumption appears to be that the Venera 4 radioaltimeter either malfunctioned or was misinterpreted (e.g., its signal at twice 26 km was taken as meaning a 26-km altitude), and that the Venera 4 telemetry did not extend to the surface (ref. 2-22). Thus, the conditions at the surface can be approximated by extrapolation. (See figs. 2-15 and 2-16.)

[….]Never-theless, in the absence of the Venera measurements, the Mariner results, which are firmly associated with a range scale, could have been extrapolated to give the surface conditions almost as accurately as they are now known. If Mariner 5 had not been flown, the original erroneous interpretation of the Venera data would not have been suspected, and the resulting theories regarding the bottom of the atmosphere obviously would be wrong.

Note the question mark:

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From Wikipedia:

Altitude of the Venera probe relative to the surface was measured during using a radar altimeter operating at 770 MHz. The altimeter had an integer ambiguity of 30 km: that is, the same radar signal would be given at an altitude of X, X plus 30 km, X plus 60 km, etc.7 (an effect known as "aliasing"). At the time the distance of the cloudtops above the surface was not known, and due to this ambiguity, the first radar return, now believed to be at an actual altitude of about 55 kilometres (34 mi), was initially misinterpreted as 26 kilometres (16 mi). Therefore, based on the (misinterpreted) radar results, the probe was initially announced by the Soviet team as a descent that ended at the surface of Venus. This result was quickly dismissed as inconsistent with the planetary diameter measured by radar, and the pressure readings by the capsule were much lower than predicted by the recently-developed models of the Venus atmosphere.


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above: The Stanford 150 foot dish (and the Moon) used to transmit the dual frequency signals to Mariner 5 for the radio occultation measurements of its atmospheric density. From instartupland.com 1, 2, 3.

Beautiful!


Mariner 5 probed the thickness of Venus' atmosphere by receiving radio signals transmitted by the 150 foot diameter dish at Stanford University. This is 1967 and there was not the Deep Space Network we know today!

Harmonically related frequencies of 49.8 and 423.3 MHz, (6.02 and 0.71 meters) were transmitted from Earth towards Venus continuously, and small antennas situated on Mariner 5's solar panels received them. This is called the Dual Frequency Experiment and these would then be called the Dual Frequency Receiver (DFR) antennas.

As the spacecraft passed behind Venus (very much on purpose) the radio beams were refracted by the venus' atmosphere. The thicker the atmosphere, the more delayed the signal, and because the atmosphere has a gradient, it is bent away from the planet.

The refraction can be expressed as $N$ the number of whole wavelengths that the beam is shifted. The quickest way to get N is to integrate the frequency shift. In addition to the normal doppler shift from spaceflight, as the beam passes through thicker and thicker atmosphere, the decreasing delay causes a "doppler" shift to lower frequency. It is this frequency shift that has been used to measure, for the first time, the extremely high density of Venus' atmosphere at the surface!

The results are discussed in The Neutral Atmosphere of Venus as Studied with the Mariner V Radio Occultation Experiments by Gunnar Fjeldbo and Arvydas J. Kliore (JPL) and Von R. Eshleman (Center for Radar Astronomy, Stanford) Ast. J. 76 (2) 1971.

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Here is a little bit of the data, where you can see refractivity $N$ and the pressure around 10 atmospheres even at 32 km!

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If this image of the cover of the report Mariner Venus 1967 NASA SP-190 is still huge, it means that imgur still hasn't fixed their bug (see: The Stack Imgur service is still not longer resizing images correctly). I'm assuming this will be rectified soon.

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  • $\begingroup$ In order to maintain the quality of the images I will not manually downsize them. I am still assuming that imgur is going to fix their bug and the medium resizing feature will be restored soon! Once it's working, I'll then return here and adjust the images accordingly. The Stack Imgur service is no longer resizing images correctly $\endgroup$ – uhoh Aug 29 '18 at 13:17
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    $\begingroup$ I took the liberty of editing this to fix a sentence that confused me, it may have been a copy/paste error. I put it back to what is in the source document. Revert if undesirable. $\endgroup$ – Organic Marble Aug 29 '18 at 14:26
  • $\begingroup$ @OrganicMarble Thanks! that's fine and please just go for it any time, it's not a liberty. I was running out of steam for the night getting this posted, and haven't proofread it yet. $\endgroup$ – uhoh Aug 29 '18 at 14:50
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    $\begingroup$ Excellent summary! Note that the raypath diagram in Fjeldbo et al. is for a hypothetical situation where the refractive index (and hence N) increases with altitude. In real atmospheres, N decreases with altitude, so the signal's path is bent toward the planet. — The photos of the Stanford dish are great. My graduate school laboratory was in the transmitter building ~100 m to the north of the antenna. You got a photo of someone "running the dish" as I did while a grad student: a bit over 4 miles roundtrip from Roble Gym, and ~500' vertical elevation gain. $\endgroup$ – Tom Spilker Sep 3 '18 at 1:54
  • $\begingroup$ @TomSpilker that's fantastic! These days I call a 500' elevation gain "hiking". The diagram may only be for the neutral part of the atmosphere where density (and presumably N) decrease with altitude for both radio and optical. But for radio, that's a great point, the ionized upper atmosphere can provide far stronger refraction than the neutral part. Currently insufficiently answered: How large does refraction become in radioastronomy? $\endgroup$ – uhoh Sep 3 '18 at 2:01

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