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# 6.9 Venus and the Greenhouse Effect

In the 1980s, a debate raged over global warming and the greenhouse effect caused by CO2 in Earth’s atmosphere. But in fact, there were two debates. One took place in scientific journals and at professional meetings, where all the strengths and limitations of the scientific method were on display. The evidence for global warming was impressive but not overwhelming. Scientists could not draw firm conclusions due to incomplete data and the limitations of computer models of the atmosphere. The second debate took place in public, and it contained aspects of politics as well as science. Some ideologues claimed that the possibility of greenhouse warming on Earth was a fraud invented by scientists and environmentalists to attract more research funding. But the greenhouse warming of Venus from a buildup of CO2 is real and directly observable.

By applying the principles of thermal equilibrium and conservation of energy, we can perform the following thought experiment: What temperature would Venus have, if it had no greenhouse effect? First, imagine that the Earth is simply moved to the position of Venus, at 0.72 AU. How much more radiant energy would the planet receive from the Sun at that distance? The inverse square law says that if Earth were 0.72 times as far from the Sun, the radiation would be (1/0.72)2 times as strong, or 1.93 times stronger.

How much would this raise the planet’s temperature? If we assume that a typical spot on Earth is 68 °F, then we can ask how much hotter it would be on Venus, if the incoming radiation were boosted 1.93 times. This is a somewhat tricky calculation, but we can approach it by thinking about the principle of equilibrium: the temperature would rise until the total energy radiated by the surface equaled the energy coming in from the Sun. Hot objects emit more radiation per unit area of their surface. This property of radiation is called the Stefan-Boltzmann law. It states that, for bodies emitting thermal radiation, the total energy radiated per unit area is proportional to T4 or the material's temperature, T, raised to the fourth power.

For example, we could say that the radiation emitted by a square centimeter of the Earth’s surface, which we designate as SEarth, would be proportional to Earth's surface temperature, TEarth raised to the 4th power:

SEarth ∝ (TEarth)4

Similarly, for Venus:

The Magellan spacecraft being prepared for launch aboard the Space Shuttle Atlantis. Click here for original source URL.

SVenus ∝ (TVenus)4

A useful trick in this kind of calculation is to divide the second equation by the first, so that we deal only with the ratios of the quantities that are changing, and the constants of proportionality cancel out. Then we get:

SVenus / SEarth = (TVenus / TEarth)4

From the discussion above, we know that the quantity on the left side, i.e. the ratio of radiation received by (and emitted by) the two planets, is 1.93. Plugging in 1.93 and solving for TVenus, we learn that TVenus will be (1.93)1/4, or 1.18, times higher than TEarth. In all physical calculations involving temperature, we must always use the absolute temperature scale, measured in Kelvins (K). The Kelvin scale is defined so that zero corresponds to no energy and no thermal radiation. This is not true of the Celsius or Fahrenheit scales. If we use 68 °F as a characteristic temperature on Earth, TEarth is equal to 293 K. Multiplying 293 K by the factor 1.18, we get the answer that Venus would be 346 K, or roughly 163 °F. This is if the temperature difference between the planets was due only to solar distance. This calculation is actually confirmed by the temperatures of spacecraft when they fly toward the Sun and approach Venus.

Thinking about the situation more carefully, you may realize that the surface of Venus is actually shaded by dense white clouds that reflect most of the sunlight back into space. So the radiation reaching the surface of Venus is even less than what we calculated above. Measuring the high reflectivity of Venus' global cloud layer, we find that Venus absorbs only about 41% of the sunlight hitting it, while Earth absorbs approximately 61%. Because Venus absorbs so little sunlight, Venus ought to be even more like Earth than calculated above. Depending on the amount of cloud cover, the temperature might be as low as 100 °F, no hotter than a summer day in some areas of the Earth.

But the measured temperature of Venus is nearly 900 °F! Why is it so much hotter than expected? Perhaps Venus has more internal heat than the Earth, which leads to a hotter surface. But this explanation fails, because Venus doesn’t have any more geological activity than the Earth. The difference can only be due to the greenhouse effect of the massive CO2 gas content in Venus' atmosphere. When the CO2 is factored into the calculation (a much more difficult set of equations), then the theoretical calculation finally gives the observed temperature.

So we can conclude that Venus is kept hot by the greenhouse effect. If there were no greenhouse effect, the only major difference in heating between the Earth and Venus would result from the fact that Venus is closer to the Sun. A planet in Venus’ position, with no greenhouse effect, would have a temperature in the general range of 100 °F to 163 °F, depending on the cloud cover, but not 900 °F. Venus thus gives us a chance to study climate modification by carbon dioxide. Of course, any foreseeable greenhouse warming on Earth would only be a few degrees, because the total amount of atmospheric CO2 is much less than on Venus. But the physical principles are well understood, and Venus proves that they work. The next time someone tries to tell you there is no such thing as climate modification by greenhouse gases, ask them why Venus has a temperature of 900 °F.

The greenhouse effect is a good example of how the study of other planets clarifies our understanding of our own planet. Venus is a kind of "natural lab experiment" that shows what happens to an Earth-sized planet when its atmosphere is altered. Venus allows us to test our theories. If we had not explored the universe around us, we would never have obtained such a clear picture of how planets' climates can evolve under slightly different conditions to be strikingly different.