Climate science has kind of had its day in court before. In 2007, for example, the Supreme Court ruled that CO 2 fits the definition of a pollutant under the Clean Air Act—a decision that forces the US EPA to draw up regulations to tackle climate change, regardless of political winds. But on Tuesday, climate science will literally have its day in court, as a federal judge receives a five-hour tutorial he requested on the subject.

The case pits San Francisco and Oakland against BP, Chevron, ConocoPhillips, Exxon Mobil, and Royal Dutch Shell. The cities are alleging that major oil companies sold fossil fuels while knowing their use would change the climate—and, critically, publicly campaigning to convince the public they would not change the climate. As San Francisco and Oakland incur significant costs building infrastructure to protect their cities from sea-level rise, they want oil companies to chip in for the bill.

The case, which would obviously set a huge precedent if the cities won, already seems to have gone further than past attempts. Other judges have booted suits on the grounds that emissions should be regulated by the EPA and therefore the issue can’t be decided in a courtroom. But the specifics of the California case—going after sellers of fossil fuels rather than local users of fossil fuels—convinced Judge William Alsup that it can go forward.

Before arguments get rolling, however, Judge Alsup made a unique request: both sides are to present the facts of climate science itself, partly by answering a list of his questions. In recent years, oil companies have publicly accepted the scientific consensus on global warming, so they are unlikely to present a contrarian view in this case. But half of this “tutorial” will focus on the history of climate science, which the companies could seek to paint as more uncertain in order to excuse their stance in the 1980s and 1990s.

As for Judge Alsup’s (surprisingly specific) questions about climate change, they’re actually fundamental to the science and quite easily answered.

Going greenhouse

Half of the judge’s questions relate to how the greenhouse effect actually works. For example, he asks, “What is the molecular difference by which CO 2 absorbs infrared radiation but oxygen and nitrogen do not?”

The term “greenhouse effect” is meant to evoke the basic result of the process rather than the actual physics involved. Greenhouses warm up by allowing sunlight in and preventing heat energy and warm air from leaving. Our atmosphere’s greenhouse effect similarly lets sunlight (mainly in the visible light portion of the electromagnetic spectrum) reach the Earth’s surface to warm it but absorbs the infrared radiation our planet emits back to space.

You’ve likely run into this explanation before, perhaps along with an analogy of building a thicker blanket around the planet that warms it up. But how does this work, exactly?

If we skip past the quantum mechanics, the simple fact is that molecules of gas can only absorb (and emit) certain wavelengths of electromagnetic radiation. Carbon dioxide—a molecule composed of one carbon atom and two oxygen atoms linked in a line—can be made to vibrate by radiation of the right wavelength. The atoms can rapidly stretch back and forth like a runaway accordion, or they can bend out of line like the “boing” of a spring doorstop when you brush against it.

Oxygen and nitrogen (which account for about 99 percent of our air) are simpler dumbbell-shaped molecules composed of two identical atoms. That removes the option of bending vibration, while stretching the bond has no effect on the electric field (the atoms are identical). So these gases can’t interact with radiation in the infrared portion of the spectrum.

CO 2 , along with the other gases we call greenhouse gases, happens to absorb infrared radiation but not solar radiation. If our planet had no atmosphere, there would be a simple balance of incoming and outgoing energy. Sunlight would warm the Earth’s surface, which would subsequently emit an equivalent amount of energy as infrared radiation sent back into space. The addition of greenhouse gases changes this by absorbing outgoing infrared radiation, warming up, and then emitting infrared energy both out to space and back down toward the Earth’s surface.

As the surface temperature increases, the planet emits even more infrared radiation, attempting to shed heat. Eventually, a new balance is achieved, with outgoing energy equaling the incoming sunlight again, but only after the temperature of the surface and atmosphere have risen. Similarly, a blanket will warm you up in winter, but it won’t unceasingly raise your temperature to the point you burst into flames.

While CO 2 lets solar radiation through unperturbed, other gases do interact with it. Ozone—which, as it's composed of three oxygen atoms, can do some vibrational quantum dancing—absorbs ultraviolet radiation in sunlight. In addition to acting as planetary sunscreen, this also causes the ozone layer to warm the stratosphere.

Water vapor is also a potent greenhouse gas, but it can form sunlight-reflecting clouds—meaning water vapor can either cool or warm the Earth, depending on the situation. (Though the net effect of water vapor amplifies global warming caused by CO 2 rather than dampening it.)

Another of Judge Alsup’s questions is a fairly common one: “Apart from CO 2 , what happens to the collective heat from tailpipe exhausts, engine radiators, and all other heat from combustion of fossil fuels?”

Given that it’s called “global warming,” it’s tempting to wonder if the heat we produce is as important as these invisible and abstract greenhouse gases. It actually doesn’t take much math to work out the answer, though. The total energy being used by humans is currently close to 20 terawatts. Assuming it is all eventually converted to waste heat, that would come out to about 0.04 watts per square meter of the Earth’s surface. The total amount of energy being added to our climate by human activities, meanwhile, was estimated at 2.3 watts per square meter in the last Intergovernmental Panel on Climate Change report.

So the warmth coming out of your car’s tailpipe isn’t the concern. The carbon dioxide is.

Altered carbon

Judge Alsup’s questions also touch on contributors to the CO 2 increase we’ve measured. Apart from simply asking for the main cause of that increase, he asks how much CO 2 is exhaled by humans and why plants haven’t simply turned all the extra CO 2 into oxygen.

These are questions about the carbon cycle—the many interconnected processes by which carbon changes forms and moves throughout the Earth’s atmosphere, oceans, land ecosystems, and even rocks. When all these processes are balanced (which was basically the case before the Industrial Revolution), the amount of CO 2 in the atmosphere stays steady. When we began to pull fossil fuels out of the ground and combust them into CO 2 at a massive scale, the carbon cycle was no longer balanced.

There are multiple ways to work out the cause of rising CO 2 . First off, there’s simple accounting. Researchers work hard to estimate how much CO 2 is being released by human activities and then compare it to measured changes in the atmosphere, oceans, and land ecosystems. In 2016, for example, it was estimated that human activities released about 11.2 billion tons of carbon, of which the ocean and land ecosystems soaked up about 5.3 billion tons. (The dissolving of CO 2 into the oceans is no free lunch—it’s changing the pH of seawater and threatening marine ecosystems.) The remainder matches the increase in atmospheric CO 2 .

This accounting can be informed by analyzing the isotopes of carbon in atmospheric CO 2 —which can be carbon-12, carbon-13, or carbon-14. Since the start of the Industrial Revolution, the relative proportions of these isotopes in the atmosphere have been changing in a way that can only be explained by chucking tons upon tons of carbon-12-dominated fossil fuel CO 2 into the sky.

Judge Alsup’s guess that plants should take CO 2 out of the atmosphere is a good one. Life has indeed reduced our impact on atmospheric CO 2 by soaking up some of it. But photosynthetic growth is limited by much more than just the availability of CO 2 (things like water and nutrients matter); otherwise, plants would simply consume all the CO 2 in the atmosphere.

However, the judge guesses incorrectly when he wonders if human respiration could be a significant source of CO 2 . Unless your diet is full of coal, the carbon you exhale ultimately comes from plants (even if you ate the cow that ate the plants), and plants simply borrowed that carbon from atmospheric CO 2 . So breathing can’t raise atmospheric CO 2 any more than your gas station’s “take a penny, leave a penny” tray can increase the number of coins in circulation.

Whodunnit? Wedunnit, duh.

Judge Alsup’s questions also touch on past ice-age cycles in climate and the dominant source of our current warming trend—why did climate change in the past, and why is it changing today?

The rhythmic ice ages of the last several million years were governed by slow-changing cycles in Earth’s orbit around the Sun, which sometimes conspired to bring stronger sunlight to the great ice sheets of the Northern Hemisphere. Shrinking ice sheets shifted the carbon cycle in a way that raised atmospheric CO 2 , further warming the planet.

Those orbital cycles are much too slow to explain what we’ve seen over the last 150 years, and records show that sunlight has not grown stronger. When you compare all the factors that could possibly warm or cool the Earth, it becomes abundantly clear that one factor explains the bulk of modern warming: our greenhouse gas emissions.

While there may be some differences in what the two sides in the case present, there is very little room to dance around these basic facts. As a non-expert, Judge Alsup has asked reasonable questions that should provide him with a rudimentary understanding of climate science. But this hearing will leave us a long way from knowing whether this understanding actually plays a role in the case.