Does the location of the Earth's orbit change when the Sun evolves into a Red Giant?

(by Amara Graps)

Many people know that astronomers predict that the Sun will evolve into a Red Giant at the end of its lifetime. But what will happen to the Earth's orbit before, during and after the Red Giant phase? On this page we take a cursory look at the Sun-Earth system during the Sun's evolution.

Mass Loss.

Does the Sun expand due to mass loss?

The Sun will not expand due to mass loss ... There are other processes that cause its expansion.

And mass loss occurs due to hydrogen conversion (about 1020 grams of Sun mass is lost every year) and due to an increase in its "solar wind" near the end of the Sun's life and due to a "sloughing" of its outer layers during the helium flash.

Angular Momentum

With a transfer of angular momentum from the Sun to the Earth, the location of the Earth's orbit increases radially further away from the Sun, but these changes are on order of centimeters, and those changes become less over time.

What is the role of conservation of angular momentum?

If the Sun's rotation slowed down, then the Earth's rotation would speed up due to conservation of angular momentum. And as the Earth's rotation speeds up, the Earth's orbit would gradually spiral away from the Sun. This is what has happened.

The period of one solar rotation was about 2 weeks when the Sun was 1 billion years old (Noyes, pg. 26), and now the period of one solar rotation is about 1 month. However, the changes in the increase of Earth's orbit were, and are, very tiny: In the past, the Earth was orbiting closer to the Sun (centimeters?).

Over time, the changes in rotation are less noticeable. During the Sun's lifetime on the main sequence, the Sun's rotation has been relatively stable. As time progresses, the rate of transfer of angular momentum becomes less and less, therefore, the Earth "spirals away less and less" due to angular momentum.

The Sun's Radius.

During the Sun's lifetime, astronomers think that the following happens to the Sun's radius.

The reason that the Sun expands is due to a causal chain of events between events in the Sun's core and events in the Sun's outer shell. We should look first at the reasons that the Sun is at the radius that it is now, and under what conditions.

Why is the Sun at the particular radius that is now?

The present radius of the Sun has just the right value to maintain a central temperature which provides a fuel generation rate (i.e. rate of nuclear energy that is caused by hydrogen "fusing" into helium) that _exactly balances_ the heat leakage rate due to the random walk of photons from the Sun's center to the Sun's surface (Shu, pg. 94). The term "random walk" means that a photon moving outwards will encounter matter and other photons, much like a billiard ball encounters matter and other billiard balls on a pool table.

What happens to the radius when the hydrogen fuel is gone?

When the hydrogen fuel is gone, that source of energy (fusion) which formerly compensated against the Sun's own gravitational pull, is now gone. The core contracts. As a ball of self-gravitational classical gas contracts, it becomes hotter (not colder) (Shu, pg. 91). In the shell surrounding the core, pressure increases in order to compensate for the increasing gravity of the core, some other complicated processes cause the intermediate shell layers to heat up, and the total radius of the Sun expands.

What happens to the Sun's radius _before_ the hydrogen fuel is gone?

The demise of the hydrogen fuel at the Sun's core is a _gradual_ process, causing a gradual increase in brightness, radius, and surface temperature of the Sun. The Sun currently is about 40% more luminous (Noyes, pg. 27), 300 degrees K hotter at its surface, and about 6 percent greater in radius than it was as a newborn star. During the last 1.5 billion years of the Sun's life, its radius will be about 3.3 times its present size, and the very outer portion of the Sun's surface will cool (Noyes pg. 27). Meanwhile, the surface of the Earth will be about 100 degrees F hotter than its present temperature and all of the oceans will have boiled away.

The Sun's End-state.

When all of the hydrogen fuel is gone, the Sun rapidly will become a red giant star. Within a "short" period of time (say 250 million years) the Sun's radius will swell to 100 times its present size, the Sun will be about 500 times more luminous, and the surface temperature will drop to about 3500 degrees K (Noyes, pg. 28). The core will be then so hot that helium ashes at the cores will ignite, and a "helium flash" will send shock waves through the Sun, blasting about a third of the body into space. Then the Sun will be burning helium at its core.

Gradually the Sun will go through the burning process again (shorter this time, and will some burning of hydrogen occurring in the shell), but it will have lost quite a bit of mass from the helium flash and from its solar wind. Eventually the outer layers will dissipate, leaving the core hot and exposed and the Sun as a white dwarf. In its final state, the Sun will contain about 1/2 of its current mass.

There is a similar description with some pictures here.

Now what about the location of the Earth at the Sun's end-state?

Life on Earth will already be dead sometime during the Sun's last one billion years :( so perhaps we won't care ...

But the Earth will (perhaps .. if some other process didn't affect it) continue in its orbit around the Sun, and perhaps *only slightly* further away than it is now.


Shu, Frank, _The Physical Universe_, University Science Books, 1982.

R.W. Noyes, "The Sun," chapter in _The New Solar System_, Beatty and Chaikin ed., Sky Publishing Corporation, 1990.

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Special Thanks to A. Graps