Does Earth accelerate towards you?

Does Earth accelerate towards you when you jump from a height? You may find it hard to believe but the answer is yes. You don’t see the acceleration since it is very small, but you do move the Earth just as the Earth moves you due to gravity. Let me explain.

Does Earth accelerate towards you? Professor Mac is shown jumping from a step towards the Earth.

There are equal and opposite forces on Professor Mac and the Earth due to gravitational attraction.

There is a gravitational force between all objects with mass. The simple fact that an object has mass means that it will attract other objects with mass. The magnitude of the force of attraction between the objects depends on their masses. The larger the masses of the objects, the larger the force of attraction. Your weight is the attractive pull force between you and the Earth.

There is a law of physics called Newton’s third law of motion. This law means that the magnitude of the force on you due to the Earth pulling on you, is the same magnitude as the force on the Earth due to you pulling on it. In other words, there are two forces acting and they are equal in magnitude; one acting on you and the other acting on the Earth.

What happens when you jump?

Does Earth accelerate towards you? Professor Mac is jumping from a step and the forces on him and on the Earth are shown by red arrows.

When you jump from a height, the Earth accelerates towards you.

When you jump off a raised step you find yourself falling towards the ground. When you are falling you are accelerating towards the Earth due to the pull force of the Earth on you. Since there is also an equal force on the Earth, it starts to accelerate towards you. However the effect of these two forces on you and on the Earth are rather different and this is due to the relative difference in the mass of you compared to the Earth.

Earth accelerates towards you

The mass of the Earth is approximately 6,000,000,000,000,000,000,000,000 kg. Yes that is 24 zeros after the figure 6! Now the average human has a mass of 62 kg. So the mass of the Earth relative to you is incredibly large. From Newton’s second law of motion we know that for a given force on an object the acceleration reduces as the mass of the object increases. Therefore it is easy to see that the acceleration of the Earth compared to you when you are falling is incredibly small. However the Earth still accelerates towards you even if it is very small.

So go on, jump a little and move the Earth.

Mac

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