Mystery of Earth not revolving around the Moon

physics

There is a famous saying by Newton, “What we know is a drop; what we don’t know is an ocean.” This great physicist of all time is a true genius ever to be born. He gave us the famous law of gravitation, the laws of motion, calculus and much more to cherish. Although there is a lot to learn from Newton, we will aim to understand the motion of the moon around the earth in the lines which follow.
We all know that the moon revolves around the earth, but what makes it revolve around the earth, and why wouldn’t the earth revolve around the moon? Or say, why wouldn’t just like the earth, the moon revolve around the sun? Why do the planets revolve around the sun, and why do the moons of planets revolve around that particular planet only? Baffling questions which make us wonder about the celestial bodies and their behavior. So, let’s get to the bottom of the problem and try to figure out how these astronomical bodies have been working perfectly and constantly day in and day out for millions of years.
This system of the moon revolving around a planet is based on the concept of center of mass. But what is center of mass? Well, the center of mass is the point around which two planets have their orbits.
If two bodies have equal masses, then the center of mass is located in the middle of them. This is the case with Pluto and its natural satellite Charon. It’s also the case of binary asteroids and the stars. But if one of the bodies is heavier than the other, then the center of mass shifts closer to the heavier body. Just like in the earth–moon system, the earth is much heavier as compared to the moon, and as a result, the center of mass of the earth–moon system lies inside the earth at a distance of about 4300 km—which is approximately 75% of the earth’s radius—from the center of the earth. So, we are unable to see the orbital motion of the earth around the center of mass, but the moon is at a considerable distance from the center of mass of the earth–moon system. Hence, its orbital motion is quite visible.
Now let’s come to the question of why the moons of different planets are still revolving around their planet and not attracted towards the sun, which is much more massive than the planets. The law of gravitation says that the larger the mass of the object, the greater would be the force of attraction between the objects. Interestingly, the sun contains about 99.8% mass of the solar system. So, shouldn’t it be able to snatch the moon away from the earth? It’s true that the sun attracts the moon with twice the gravitational force as compared to the earth, yet the moon doesn’t leave the earth but continues to faithfully orbit around it. This happens because every planet has a region with which it dominates the attraction of its satellite. This special region is called the hill sphere. So, to be retained by a planet, a moon should lie within the planet’s hill sphere. In more precise terms, the hill sphere approximates the gravitational sphere of influence of a smaller body when faced with perturbation from a more massive body. The hill sphere of the earth is about 1.5 million km and the moon revolves around the earth at about 0.384 million km. So, our beloved moon is not going to be pulled by the sun. It’s safely ours. This same theory applies to every planet and its many moons.

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