THE SOUTHWORTH PLANETARIUM
207-780-4249      www.usm.maine.edu/planet
70 Falmouth Street     Portland, Maine 04103
43.6667° N 70.2667° W
Founded January 1970
Julian date:  2457756.16

"The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift." -Albert Einstein

THE DAILY ASTRONOMER
Wednesday, January 4 2017

Losing the Moon?

Pandora's Jar is our self-replenishing cornucopia. We remove a piece of parchment, answer the question written on it and -to our delight- find that the answer has spawned other questions that we stuff into the Jar for future withdrawal. The answers to those questions will, in turn, inspire other questions and the spawning will continue ad infinitum. In fact, we suspect that we'll never see Pandora's Jar emptied of its parchments. We wouldn't have it any other way.

The first Pandora parchment of 2017 is question sent to us in response to the answer of a previous Pandora. This fascinating question brings us into the remote future. It asks us if our one natural satellite could ever leave us completely.

PANDORA PARCHMENT # 12:

"The moon is moving away from Earth at a slow rate. Over time, however, could the moon move far enough away that it could be captured by the Sun's gravity and no longer orbit our planet?"

-A.G, Raymond, ME

Greetings! This being a "yes or no" question, we can offer a simple answer. "No, we'll never lose the moon." However, such a thoughtful question deserves a more thoughtful answer. Also, researching the answer led us to a startling discovery about the moon's possible fate!

First, we should explain that the moon is receding from Earth at the rate of 4 cm (1.6 inches) per year. Frictional forces exerted between Earth and moon both retard the planet's rotation rate and cause the moon to move slowly away from us. (At some later date we can delve into the fascinating physics behind this recession.) The moon will continue to recede from Earth until both bodies establish a state of gravitational equilibrium known as "mutual synchronous rotation." The moon's average distance at this stage would be about 340,000 miles. The Sun will, however, perish before the moon ever reaches this state of mutual synchronous rotation.

Now, could the moon be captured by the Sun even before our satellite reaches this distance? No, it could not. Earth's gravity will always dominate the moon, even though the Sun is far more massive. Here we should explain the concept of the "Hill Sphere," which is defined as a region around any orbiting body in which its gravitational influence will prevail over that of the body it orbits. Calculations reveal that Earth's Hill Sphere extends out to about 943,000 miles from Earth. Any satellite within this region cannot establish an orbit around the Sun.

The "Hill Sphere." Earth revolves around the Sun, which is about 332,000 times more massive than our planet. However, bodies within Earth's "Hill Sphere" will be retained by its gravity and cannot establish an independent orbit around the Sun. Calculations (which we let other people perform because we're truly generous like that) show that the radius of Earth's Hill Sphere is about 943,000 miles. The moon will never move out of Earth's "Hill Sphere" and, therefore, we'll never lose it.

We determined earlier that the moon's greatest possible distance from Earth is approximately one-third of Earth's "Hill radius." The moon won't even reach that distance before the Sun perishes, so we can assure you that the moon will always be Earth's satellite.

Perhaps we should qualify that "always" statement. It is possible that the moon could actually move back toward Earth. When the Sun exhausts its core hydrogen reserves, it will expand as a red giant. If the expansion pushes the bloated Sun's outer layers out toward the Earth region, Earth and the moon could be enveloped in those rarefied solar gases. The resultant drag could cause the moon's orbit to decay. If the orbit decay causes the moon to move to within 11,451 miles of Earth -the planet's Roche limit- the moon will actually break apart and its fragments will form a ring around the planet.

However, that fate is highly speculative. Astronomers still can't know the extent of the Sun's expansion or how the Earth-moon body will respond to this expansion.

Suffice it to say, A.G., that Earth will always keep its moon.