Nine cities across the United States, including New York and San Francisco, have taken the bold step of filing lawsuits against oil companies for damages stemming from climate change, arguing they are under threat from sea level rise and increasing heat waves.

Unlike previous cases where climate change has gone to court, the science itself isn’t on trial. In fact, the oil companies largely agree with the plaintiffs on the science and humanity’s role in rising temperatures. What will be debated here is the question of liability for the impacts of climate change, a much murkier legal issue and one with huge financial consequences for the energy sector.

To prepare for it, William Alsup, the judge presiding over two of the lawsuits — filed by San Francisco and Oakland against Royal Dutch Shell, BP, ConocoPhillips, Chevron, and Exxon Mobil — has scheduled a five-hour tutorial on climate science this Wednesday.

The tutorial is a big deal: It will set a federal judicial precedent establishing the facts of the mechanisms of global warming.

The lesson will come in two parts: The first part will give both sides — the San Francisco and Oakland city attorneys, and representatives of the oil companies — 60 minutes each to present the history of the study of climate change. The second part will again give both parties an hour to present the best available science on global warming, melting ice, sea level rise, and coastal flooding. The litigants are allowed to have experts or attorneys make the presentations.

While the tutorial will focus on basics like how infrared radiation trapped by carbon dioxide in the atmosphere is turned into heat and finds its way back to Earth, it will build a foundation for future litigation on the impacts of rising temperatures around the world, particularly lawsuits stemming from harm to the environment or human health from climate change.

Alsup has posted eight questions on climate science that he wants to address in the tutorial, some of which are very basic and others of which are highly technical.

“These feel like very solid-ground questions,” said Daniel Kammen, a professor of energy at the University of California Berkeley who is also a likely witness in a separate climate change lawsuit. “They’re trying to establish a baseline for dialogue.”

A basic science tutorial in a courtroom is unusual but not unprecedented for Alsup, who likes to establish a common set of facts before a case moves forward.

As a judge at the United States District Court for the Northern District of California, Alsup frequently hears highly technical cases from Silicon Valley and isn’t afraid to wade into the weeds.

The 72-year-old judge codes in the programming language BASIC and dabbled in Java ahead of the Oracle v. Google lawsuit in 2012, as Sarah Jeong wrote in her fantastic profile at The Verge. Last year, he also asked for a tutorial on lidar systems while presiding over the self-driving car intellectual property lawsuit between Waymo and Uber.

Alsup is right that it can get complicated connecting the dots from carbon dioxide’s infrared radiation absorption to sea level rise in San Francisco.

So, may it please the court, I’ve answered his honor’s questions with the help of several climate scientists.

1) What caused the various ice ages (including the “little ice age” and prolonged cool periods), and what caused the ice to melt? When they melted, by how much did sea level rise?

Short answer: The Earth, very slightly, very slowly, wobbles as it spins, changing where sunlight hits the planet such that it allows ice sheets to form or melt.

Long answer: If you’ve ever spun a top, you may have noticed that it can stay upright even as it wobbles and that the spindle can trace circles as the whole top spins.

The Earth undergoes similar deviations as it orbits the sun, like in the shape of its orbit, the tilt of its axis, and its wobble (a.k.a. precession). But these shifts, known as Milankovitch cycles, occur on times scales from 23,000 years to 100,000 years.

The effect of this is that sunlight can hit Earth in different places during certain phases of the cycle. When less sunlight hits the polar regions, less ice melts in the summer and more accumulates in the winter, allowing the ice sheets to grow. A larger swath of ice then has knock-on effects for the rest of the planet as less water remains liquid and air currents sweep cold temperatures to the rest of the planet, creating an ice age.

When more sunlight starts hitting the poles again at the end of an ice age, the ice starts to melt. Since the last ice age 19,000 years ago, global sea levels have risen by more than 120 meters, which gives you an idea of just how much water was and remains stored in ice.

If the current ice sheet on Greenland were to melt, it would raise global sea levels by 6 meters.

The “Little Ice Age,” a period of cooling in North America and Europe between 1300 and 1800, is actually a separate phenomenon from true ice ages, and it occurred on a regional rather than global scale. Scientists are still figuring out why it happened, but there is some evidence that it started due to volcanic eruptions and ended with a change in output from the sun.

2) What is the molecular difference by which CO2 absorbs infrared radiation but oxygen and nitrogen do not?

Short answer: A carbon dioxide molecule (CO2), which has three atoms from two different elements, vibrates in a way that absorbs infrared radiation. Molecules of nitrogen gas (N2) and oxygen gas (O2) are made of two atoms of the same element and don’t vibrate in the same way.

Long answer: In order to absorb in the infrared spectrum, a molecule has to vibrate in a way that creates a separation of positive and negative charges known as a “dipole moment.”

Carbon dioxide is made of one carbon atom and two oxygen atoms. The oxygen atoms have a greater affinity for electrons than carbon, creating a charge gradient, but since they are on opposite sides of the carbon in a straight-line configuration, the gradients cancel out, so there is no dipole moment in carbon dioxide’s ground, or unexcited, state.

However, when carbon dioxide receives an energy input, it can bend or shake in a way that forms a charge gradient, creating a dipole moment in its excited state, thereby allowing it to absorb infrared radiation.

Water, which is made of hydrogen and oxygen, has a “bent” structure, creating a permanent dipole moment in its ground state. Not surprisingly, water is also a greenhouse gas.

In fact, water vapor is the most abundant heat-trapping gas on Earth, but the amount of water isn’t increasing and vapor only lasts about 10 days in the atmosphere before it falls away as precipitation. It doesn’t accumulate like carbon dioxide, which can linger for 200 years in the atmosphere, so water vapor is not the driver of the current warming trend, though it creates a warming feedback.

Larger, more unbalanced molecules like chlorofluorocarbons are even better at trapping heat.

Meanwhile, nitrogen gas is made from two nitrogen atoms stuck together. Since the nitrogen atoms have an equal affinity for electrons, they share them evenly, so there is no dipole moment, rendering the gas invisible to infrared. It’s the same story for oxygen gas. And molecules with three atoms like water and carbon dioxide have more ways to vibrate, or “modes,” than molecules with just two atoms.

That’s why carbon dioxide is the main culprit behind the changes in the climate we’re seeing, even though nitrogen and oxygen make up more than 90 percent of the atmosphere and water vapor is a more abundant heat trapper.

3) What is the mechanism by which infrared radiation trapped by CO2 in the atmosphere is turned into heat and finds its way back to sea level?

Short answer: Sunlight hits Earth’s surface and is reflected back toward the atmosphere as infrared radiation, where carbon dioxide absorbs it and reemits it toward the Earth.

Long answer: The mechanism at work is the fundamental greenhouse effect that keeps Earth from freezing into a ball of ice. This is also the reason the planet Venus is hotter than the planet Mercury, even though Venus is farther from the sun.

Solar radiation travels 93 million miles from the sun to the Earth through the vacuum of space and passes through Earth’s atmosphere. Some of the ultraviolet light is absorbed by the ozone layer, and clouds reflect some of the light back into space.

The solar energy that makes it through the sky warms the planet’s surface, causing the surface to radiate heat in the infrared spectrum. This radiation is emitted into the atmosphere, where it strikes carbon dioxide molecules. As you can see in this animation, carbon dioxide both absorbs and emits infrared light:

Some of that infrared radiation is reemitted into space, but some is sent back to the Earth’s surface, trapping heat. Without the greenhouse effect, the average temperature of the Earth would be –18° Celsius (0° Fahrenheit).

4) Does CO2 in the atmosphere reflect any sunlight back into space such that the reflected sunlight never penetrates the atmosphere in the first place?

Short answer: Not really.

Long answer: Since carbon dioxide is an invisible gas, it doesn’t absorb or reflect light in the visible spectrum. It does reflect some solar energy back into space, but the amount is too small to matter to greenhouse effect calculations.

5) Apart from CO2, what happens to the collective heat from tail pipe exhausts, engine radiators, and all other heat from combustion of fossil fuels? How, if at all, does this collective heat contribute to warming of the atmosphere?

Short answer: It’s negligible.

Long answer: In 2015, humanity produced 13,647 million tons of oil equivalent energy, or 158,714 terawatt-hours of energy. Assuming that all of this energy eventually ends up as heat, that means if you were to add up all the artificial heat sources on the planet — radiators, refrigerator coils, furnaces, boilers, and so on — over the course of the year and divide by the area of the planet, you would get a paltry warming rate of 0.035 watts per square meter. Net warming from greenhouse gases is 2.3 watts per square meter, about 65 times more than all those direct heat sources combined.

6) In grade school, many of us were taught that humans exhale CO2 but plants absorb CO2 and return oxygen to the air (keeping the carbon for fiber). Is this still valid? If so, why hasn’t plant life turned the higher levels of CO2 back into oxygen? Given the increase in human population on Earth (4 billion [since the start of the Industrial Revolution]), is human respiration a contributing factor to the buildup of CO2?

Short answer: Plants are indeed growing more because of increased carbon dioxide, but it’s not enough to offset the increases. And humanity’s breaths don’t move the needle of atmospheric greenhouse gas concentrations.

Long answer: Your grade school teachers are still right. About a quarter of human-produced greenhouse gas emissions are absorbed by plants, and some plants are responding to increases in carbon dioxide concentrations by growing more and producing more oxygen. But increased carbon dioxide fertilization also has side effects for plants like increasing pollen production and reducing nutrients in crops. And there aren’t enough plants on Earth to soak up all the carbon dioxide we’re pumping out.

As for the 7 billion people breathing out carbon dioxide every day, they really aren’t an important factor in global warming. Overall biomass does impact the concentrations of carbon dioxide in the atmosphere, but humanity is a tiny sliver of life on Earth.

And living organisms are part of the carbon cycle. The carbon they consume as fuel and emit as they breathe and release when they die forms a closed loop, so the overall amount of carbon in the biosphere remains the same. What changes the balance is the introduction of carbon into the biosphere that was previously locked away underground for millions of years, i.e., combustion of coal, oil, and natural gas.

So unless you’re powered by gasoline, there’s no need to hold your breath.

7) What are the main sources of CO2 that account for the incremental buildup of CO2 in the atmosphere?

Short answer: Take a wild guess. Completely off the wall.

Long answer: Perhaps a more interesting way to ask this question is how do we know the increases in carbon dioxide come from burning fossil fuels.

We know this because we have a good handle on how much fossil fuel we extract and burn. Coal, oil, and natural gas companies obviously want to keep track and how much they produce, and the amount of carbon dioxide increasing in the atmosphere aligns most closely with how much fossil fuels we burn.

And like crime scene investigators, scientists can do a forensic analysis of greenhouse gases in the atmosphere. Fossil fuels have a distinct fingerprint in the isotopes of their carbon. An isotope is a version of a chemical element that has the same number of protons but a different number of neutrons in the nucleus.

So after sampling atmospheric carbon dioxide and comparing the isotopes, scientists know they have fossil fuels dead to rights.

8) What are the main sources of heat that account for the incremental rise in temperature on Earth?

Short answer: Heat trapped by human-produced carbon dioxide is driving most of the warming we’re seeing.

Long answer: On balance, the changes humanity is making to the world are causing the planet to warm, though some human-produced substances like aerosols can also have a cooling effect:

Another way to ask this is how do we know the bulk of the warming we’re seeing isn’t caused by anything other than fossil fuels. Bloomberg produced an excellent visualization comparing the observed temperature changes on Earth to factors like volcanic activity, changes in solar irradiance, and shifts in the Earth’s orbit:

Greenhouse gases from fossil fuels again stand out as the main cause of climate change. That’s why the Intergovernmental Panel on Climate Change said it is “now 95 percent certain that humans are the main cause of current global warming.”

Special thanks to Glen Peters at the Center for International Climate Research, Gavin Schmidt at NASA, and Andrew Dessler at Texas A&M University.