Hail Mary Science
Light, heat and climate

Solar luminosity simulator

This model shows what would happen if the Sun dimmed steadily, at a compounding rate on the order of 0.3% a year. It isn't an astronomical forecast, since the real Sun is very stable. It's a way to see how sensitive the climate is to small changes in the energy we receive.

Key formula

L(t) = L₀ · e^(−k·t) · T_planet ∝ L^(1/4)

Try it

How to use the simulator

This model shows what would happen if the Sun dimmed steadily, at a compounding rate on the order of 0.3% a year. It isn't an astronomical forecast, since the real Sun is very stable. It's a way to see how sensitive Earth's climate is to small changes in the energy we receive.

Controls

  • Years from now: 0 to 100. The Sun's disc shrinks and the panel shows the remaining luminosity and its rough effect.

Things to try

  1. Check how many years it takes to lose 5%. That sounds small, yet the panel already links it to an ice age.
  2. Compare it with the real 11-year solar cycle, during which luminosity changes by only about 0.1%.
  3. Move to 100 years and notice the decline slowing down: each year loses a percentage of what's left, not a fixed amount.

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The real Sun is very stable

The energy reaching the top of Earth's atmosphere from the Sun is about 1,361 W/m², the so-called solar constant. Over the 11-year solar cycle it varies by only 0.1%. Over billions of years the Sun slowly brightens: 4 billion years ago it put out about 70% of what it does today.

There is no known mechanism for a fast, sustained dimming like the one this tool simulates. That is exactly why it makes a good thought experiment for understanding the link between sunlight and climate.

Why a small percentage matters so much

A planet's equilibrium temperature goes with the fourth root of the energy it receives. 5% less light cools the surface by just over 1% of its absolute temperature: about 3–4 °C before any amplifying effects.

But there are amplifiers. As it cools, the area covered by ice and snow grows, which reflects more light and cools things further. During the last ice age Earth was only about 6 °C colder than today, and ice covered much of Europe and North America.

Worked example

Example: how long to lose 5%?

  1. With a 0.3% compounding yearly loss: L = 100 · e^(−0.003·t).
  2. To reach 95%: t = ln(1 / 0.95) / 0.003 ≈ 17 years.
  3. The direct effect on temperature: (0.95)^(1/4) ≈ 0.987, i.e. 1.3% lower. On a 288 K average, about 3.7 °C colder.
  4. After 100 years 74% would remain: each year loses a percentage of what is left, not a fixed amount, which is why the curve flattens out.

In Project Hail Mary

The novel's starting point is that the Sun begins to lose brightness measurably, and scientists work out what that will mean for Earth's climate within a few decades.

This tool appears in:Chapter 2The Pendulum and the Dying Sun

Frequently asked questions

Is the Sun dying out?

No. It has about 5 billion years left in its current phase and, in fact, it is brightening very slowly, by about 1% every 100 million years.

Do sunspots change the climate?

Very little. The sunspot cycle shifts solar output by about 0.1%, a small effect compared with rising greenhouse gases.

What was the Maunder Minimum?

A period from 1645 to 1715 with almost no sunspots. It overlapped part of the Little Ice Age, although studies attribute that cooling mostly to volcanic eruptions.

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