The physics of the "Supermoon", part 1

A LOT of my students are talking about the so-called "supermoon" that will happen on Friday. Basically, the Moon will be at perigee, or closest point to Earth in its orbit, and also in full moon phase.

In other words, the Sun, Earth, and Moon will be in the following position:

I'm not sure where the claim started, but someone is trying to convince the public that the world is going to end (or, at minimum, there will be some horrible earthquakes/tsunamis) around Friday.

Such a bold claim, especially one that comes on the heels of an absolutely horrible earthquake and tsunami in Japan, better be backed up by some outstanding evidence. Let's see what high school physics has to say.

Newton's Law of Universal Gravitation is

whereis the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. This works just about anywhere in the universe, and definitely works for objects in our solar system.

[Note: The units are all SI. Newtons (N) are a unit of force; 1 N ~ 0.225 lbs.]

Think about the force on a single mass, say a person of mass mp = 100 kg, at the surface of the Earth. There are three significant gravitational forces acting on him: the forces of gravity between him and the Earth, between him and the Sun, and between him and the Moon.

The force of gravity between the Earth and that person (mp = 100 kg) is

where is the mass of the Earth, and the distance between the masses is the radius of the Earth, . Using these numbers, I get

The Earth's orbit around the Sun is nearly a circle, so I will treat the distance between the Sun and the Earth to be a constant. The force of gravity between the person on Earth's surface and the Sun is

where is the mass of the sun, and  is the distance between the Sun and the Earth. 

Again, using these numbers,

This is much smaller than the force of gravity from the Earth. (If it were larger, then we'd float off Earth's surface and eventually fall into the Sun.) 

What about the force of the Moon on the person? Because the moon has a more elliptical orbit, its distance from the Earth changes enough that it's worth checking the magnitude of the force when the Moon is closest to the Earth and when it is the farthest away. 

The force between the person on Earth's surface and the moon at its closest (as in the Moon's position around March 18) is

with is the mass of the moon, and  is the distance to the Moon when it is closest to Earth. [In astronomy, we call this lunar perigee.] Using these values, the force the Moon exerts on our person on Earth is

This is much smaller than even the force from the Sun. 

Now, the force exerted by the Moon on the person on Earth when the Moon is at its farthest distance is given by a nearly identical expression, where we replace the distance for closest approach with the greatest distance between the Earth and Moon: [Astronomers call this 

lunar apogee.]

Using the number for the mass of the Moon used in the previous calculation, we find

Note that this is, again, a very small number. Also note that the difference, 0.00372 N - 0.00297 N = 0.00075 N is a tiny, tiny fraction of the overall gravitational force on the person on Earth. Also note that this represents the maxiumum range of effect of the Moon's gravity on Earth. 

It's easier to consider the relative strengths of these in terms of percentages. So, I'm going to divide all the forces by the force on an object due to Earth's gravity, FEarth, and multiplying by 100 to get a percentage. 

The critical figure is the last one. The change in the gravitational force due to the change in the Moon's distance from Earth is a negligible factor.

But wait - you might be saying. What about tides? They exist, and they exist in part because of the Moon! Tune in to the next post for that.