Venus’ climate IV: How scientists know Venus’ surface temperature isn’t from a "recent" astronomical collision

Artist rendition of celestial impact that formed the Moon.
Fahad Sulehria, http://www.novacelestia.com

The images returned by various robotic probes to Venus suggest that the planet’s crust is geologically young – less than a billion years old. Scientists currently believe that, because Venus has no continental drift to speak of, heat generated by radioactive decay in Venus’ core gradually builds up until it’s hot enough to melt significant portions of the crust. The resulting volcanism would release so much lava that it would largely erase geologic features that existed prior to the “resurfacing.”

Another alternative hypothesis for the young observed age of Venus’ surface is that Venus could have been impacted by a large asteroid or comet that released enough energy in the collision to resurface Venus. Many climate disruption deniers have latched on to this hypothesis because it supposedly explains how Venus’ surface could be so hot without the need for a strong greenhouse effect from carbon dioxide (CO2). But we can use some pretty simple physics to investigate this hypothesis as well.

We know from yesterday that cooling 50 km of crust from the melting point of silica (1923 K) to the modern value of 735 K should take about 86 million years. This puts the age of the hypothetical collision no more than 86 million years ago. Venus would have had to been radiating heat into space ever since. We are going to calculate three different energies and compare them to each other in order to see if they make sense. If they do, then this hypothesis is at least feasible. If the calculated energies don’t make sense then this hypothesis is disproved.

Let’s start by calculating the amount of mechanical energy in an orbiting body. The amount of mechanical energy present in an orbiting body is given by Equation 5.1

E_{orbit}=G\frac{m_{Venus}\cdot m_{Sun}}{2r_{Venus}} (Eqn 5.1)

where G is the universal gravitational constant, mSun is the mass of the Sun, and all values are defined in this table. When we calculate the mechanical energy in Venus’ orbit, we find that the total energy is -2.99 x 1033 J. The number is negative because the energy of a closed orbit is defined as negative.

We can use a simple spreadsheet to help us with the next step – comparing the total energy emitted by Venus under a black-body assumption (ie the atmosphere doesn’t impede radiation of energy into space) as it cooled over 86 million years and then we can compare the two numbers. If Venus radiated more energy than the total mechanical energy in Venus’ orbit, then we know we have a problem, because Venus would have spiraled down into the Sun as it radiated its energy away.

Energy emitted by “black body” Venus as it cools following a celestial collision.

Notice that the “Running Energy Sum” column turns red at in the fifth row – that’s the row where the total energy radiated from Venus exceeds the total energy in Venus’ orbit. It occurs approximately 220,000 years after Venus starts to cool, or about 85.8 million years ago. Since Venus hasn’t spiraled down into the Sun, there’s a problem with our assumptions somewhere.

(UPDATE: It was pointed out to me that I incorrectly equated thermal and mechanical energy. The only way that Venus could have spiraled down into the sun was if the thermal radiation was directional, and there’s no physical reason why that would have been the case. I apologize for the error.)

That’s two of the energies we’re interested in. The third is how much energy it would take to raise Venus’ crust to the melting point of silica plus how much more energy would be required to melt Venus’ crust. The sum of the two will be the total energy required to “resurface” Venus’ crust.

We can estimate the mass of Venus’ crust by first calculating the volume of Venus’ crust and then multiplying that volume by the density of silica. This is shown in Equation 5.2:

m_{Vcrust}=D_{silica}\frac{4}{3}\pi\left[r_{Venus}^3-\left(r_{Venus}-50km\right)^3\right] (Eqn 5.2)

Substituting in the values for the variables we get that the mass of 50 km of Venus’ crust is about 5.03 x 1022 kg.

Equation 5.3 shows the equation for calculating the total amount of energy required to melt 50 km of crust:

E_{melt}=E_{heat}+E_{melt}=m_{crust}[\kappa_{silica}( T_{melt}-T_{VenusBB})+H_{fuse-Si}] (Eqn 5.3)

where TVenusBB is the black body temperature of Venus calculated from Equation 2.6 (ie the temperature that Venus was supposedly at before the hypothetical collision) and the other values are defined in this table. The total energy required to raise Venus’ crust from 328 K to 1923 K and then to melt the crust is calculated to be 5.65 x 1028 J.

Halemaumau fountains and the lava lake on Kilauea’s summit at night in 1967. (USGS)

Now look at the energy in the spreadsheet capture above. Notice that the first row of “Total Energy Emitted by Venus (J)” shows that the total energy emitted in the first 46,000 years is 6.13 x 1032 J. That’s the energy emitted by Venus’ crust as it cools one degree. The energy required to melt the entire crust is 10000 times less.

We clearly have a major disconnect somewhere. It should take 86 million years or so to cool Venus from 1923 K to the modern surface temperature of Venus following a collision. yet that much energy radiated by a black body would have caused Venus to spiral down into the sun tens of millions of years ago. Furthermore, A collision powerful enough to melt the entire surface of Venus would have generated a massive amount of energy, but it would have radiated away into space after only a few thousand years when we treat Venus as a black body and ignore the planet’s atmosphere.

Obviously, the problem has to be with our assumption that Venus qualifies as a black body. The black body assumption works well under two conditions:

  1. the body is small enough that it lacks any atmosphere at all; or
  2. the body’s atmosphere does not absorb and scatter significant amounts of radiation in the primary radiation band for the hypothetical black body.

In the case of Venus, it not only has an atmosphere, it has the thickest atmosphere in the solar system, so #1 doesn’t apply. And given that Venus’ black body spectrum (at 735 K) emits strongly at the same wavelengths that the majority component of its atmosphere (CO2) absorbs at, #2 doesn’t apply either.

Venus is not a black body, its atmosphere is not transparent to infrared radiation, and so the reason that Venus’ surface temperature is so high must have something to do with its atmosphere, not its core or recent geologic history.

Tomorrow: How scientists know Venus’ surface temperature is a result of carbon dioxide-caused greenhouse heating.

Common Constants and Variables:

  • Speed of light in a vacuum: c = 299792458 m·s-1 (exact)
  • Plank’s Constant: h = 6.62606896 × 10−34 J·s
  • Boltzman’s Constant: k = 1.3806504 × 10−23 J·K-1
  • Stefan-Boltzman constant: σ = 6.669 x 10-8 5.670 x 10-8 W·m-2·K-4)
  • Universal Gravitation constant: G = 6.674 x 10-11 N·m2·kg-2
  • Avogadro’s number: NA = 6.023 x 1023 items·mol-1
  • Gas constant: R = 8.314 J·mol-1·K-1
  • Mean radius of the Sun: rSun = 6.955 x 108 m
  • Mean radius of Venus: rVenus = 6.052 x 106 m
  • Mean orbital distance from Venus to the Sun: rVorbit = 1.0821 x 1011 m
  • Mass of Venus: mVenus = 4.87 x 1024 kg
  • Mass of the Sun: mSun = 1.99 x 1030 kg
  • Approximate thickness of Venus’ crust: lcrust = 50 km
  • Average surface temperature of the Sun: TSun = 5778 K
  • Average surface temperature of Venus: TVenus = 735 K
  • Estimated temperature of Venus’ core: TVcore = 7000 K
  • Specific heat capacity of silica (SiO2): κsilica = 703 J·kg-1·K-1
  • Thermal conductivity of silica: ksilica = 1.38 W·m-1·K-1
  • Approximate density of silica: Dsilica = 2203 kg·m-3
  • Molar mass of silica: Msilica = 2.81 x 10-2 kg·mol-1
  • Heat of fusion of silicon: Hfuse-Si = 5.021 x 104 J·mol-1

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