The center of mass of any object is the average location of all its mass. For a single object, like a baseball, the center of mass is the average location of all the baseball’s mass, like the meat inside it and the heavy metal inside it.
For more complex objects like planets or moons or systems including these, the calculation gets more complicated. You have to take into account how much mass each part has, and how close it is to other parts. You have to do this for both sides as well, Earth and Moon!
Researchers from Japan’s Kyoto University recently published a paper in the journal Geophysical Research Letters detailing their efforts to find the center of mass of our planet and its moon. How did they do it? By taking precise measurements using satellite data.
Read on to learn more about their findings, as well as some other interesting facts about our planet’s center of mass.
Calculating the center of mass
Now that we know how to find the center of mass of a single object, let’s put that knowledge to use finding the center of mass of the Earth-Moon system.
As mentioned before, the Earth-Moon system is made up of five distinct bodies: Earth, Moon, Sun, Mercury, and Venus. We will not include these other bodies in our calculation as they are too far away to significantly affect the center of mass of the system.
To calculate the center of mass for any system of n objects, we need to calculate (n-1) separate centers of mass and then average them. The average point will be the center of mass for the entire system.
We will do this by first calculating the weight (mass x gravity) of each object in the system and then assigning those values to their respective objects. Then we will find each object’s coordinate on a sphere and assign those values to their respective objects.
The Earth-Moon system
A related question is how far from the Earth-Moon system’s center of mass is the center of the Earth? The answer is… pretty far!
The distance from the Earth’s center to the Moon’s center is about 385,000 kilometers. As mentioned before, the combined mass of Earth and the Moon is approximately equivalent to 10 billion trillion liters of water.
So, using that same math, we can figure out that the total mass of Earth+Moon is about 6 x 1021 kg. The average distance between Earth and Moon is about 380,000 kilometers, so that makes their relative masses 6 x 1020 kg.
Therefore, 6 x 1020 /10 billion trillion = 1 part in 1 trillion.
Mass of the Earth
Now let’s talk about the mass of the Earth. What is mass? Mass is how much matter an object contains.
We understand matter as anything that has a physical presence. This can be atoms, molecules, substances, etc. Mass is how much of these things an object contains.
The more mass something has, the more it will pull towards other masses. The less mass it has, the less it will pull towards other masses.
We use Newton’s law of universal gravitation to understand how much mass an object pulls on another object. More about that later!
The Earth has a very large mass, so it pulls very strongly on other objects that have mass. This is why we feel like we are being pulled down into the Earth when we stand on our feet. Our body is being pulled towards the center of the Earth.
Mass of the Moon
The mass of the Moon is an important factor in how much the Earth wobbles. The more mass the Moon has, the more it pulls on the Earth and the more it affects its rotation.
As stated before, when the Moon is closest to the Earth, it pulls harder on our planet. This gives us shorter days and longer nights!
Interestingly, if we didn’t have any other planets or moons in our solar system, none of this would have happened. The only thing that changed was our view of the moon. But by doing so, we saw just how much it affects us here on Earth.
We know all of this thanks to some incredible scientific experiments and research done over the past few centuries.
Distance to the center of the Earth
The distance to the center of the Earth is about 6,000 kilometers (about 3,700 miles) below the surface. This depth is called the equatorial radius.
The Earth is not a perfect sphere. It is wider at the equator than it is at the poles. This shape is called an ellipse, with it being an elongated sphere.
Because of this shape, you could walk half way around the Earth and end up at the same point you started! Weird, right?
Because we live on this planet, we take its size for granted. But if you were to visit another planet, you would need to know its diameter in order to plan your trip.
You might have heard rumors that there are places in Africa where you can fall down a hole and end up in China on the other side of the planet. That’s a myth—you would end up somewhere closer to home instead.
Center of mass vs. gravity
The center of mass of any object is the average location of all its mass. All things, including the earth and moon system, have a center of mass.
But gravity does not work at the center of mass. For example, if you dropped something on the earth’s surface directly above the earth’s center of mass, it would not hit that point; it would fall toward the earth’s surface below it.
To see how gravity works at the center of mass, imagine a very tall pencil standing on end. If you pushed it so it wobbled back and forth, you could imagine what happens when the earth rotates: It sort of spins like a top. When it does, one side — either north or south — is higher than the other.
When that side is higher, things fall north or south of the pencil. At every point in time, there are places where things will fall to either side of the center of mass.
Applications of center of mass
The center of mass is an important concept that is applied in many situations. Most notably, the use of the center of mass is seen in physics principles.
For example, the law of conservation of energy states that the total amount of energy in a system remains constant when chemical or physical changes occur. This is because energy is transferred or transformed from one form to another.
How? Energy that is transferred or transformed comes from the system’s center of mass. By looking at where all of the mass lies, you can determine where the center of mass is and what kind of energy comes from there.
This can be applied to many situations, such as studying planet rotation, how animals move, and how waves move through a system. By looking at the center of mass in a system, you can determine how it responds to stimuli.
Example problem using center of mass
Now let’s look at a physics problem that uses the Earth-Moon system as an example. Imagine that you are an astronaut in the International Space Station, which is orbiting the Earth at a distance of about 400 kilometers (250 miles) above the Earth’s surface.
You have been asked to calculate how far you are from the center of mass of the entire Earth-Moon system. How would you solve this problem?
The answer involves first calculating the mass of each object in the problem (the Moon and Earth), then calculating their distances from one another, and finally calculating the average of these distances. The average distance is what we want, because that is what defines where the center of mass is.
