# 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.

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?

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 Mac

I teach physics and engineering through animation.

### 12 Responses

1. Brendan says:

What is the relationship between, Newton’s Gravitational Constant, G, and the acceleration due to gravity, g, if any
These are the two equations I remember from 50 odd years ago
1.F=ma; Therefore w=mg and
2. F= G(m1x m2)/r squared.
I always thought, without learning, that on earth’s surface G=g

• Mac says:

Hi Brendan. You are close to calculating it with the two equations. Since w is the force of attraction between Earth and the other mass, you can make these two equations equal and therefore g =G Me/r squared. Me is the mass of Earth and r is the radius of Earth.

2. srinikesh says:

Every object in earth experience the same acceleration right(9.8m/s) .
How does this acceleration depend on mass? And a body of 92 kg and 50 kg experiences same acceleration while free falling right? So when earth pulls both towards earth it both comes in same acceleration so why does we says it depend on mass

• Mac says:

Hi Srinikeshcs. Yes all objects experience the same acceleration under the gravity force. The gravity force depends on the mass. The larger the mass the larger the force. However because the mass is higher the force needs to be higher to give the same acceleration. See my video which will explain it here.

3. jonjon says:

If you jump off of a ledge and accelerate toward the Earth, the Earth will accelerate toward you at the same time due to Newton’s Third Law. Why don’t we see the earth move in this situation?

• Mac says:

Hi Jonjon. I think the answer is in my post. Have another read of it. Think about the magnitude of the acceleration of Earth compared to you.

4. ANDREW ONYARI says:

and so how do we calculate the acceleration of earth towards a body prof?

• Mac says:

Calculate the force of attraction between them using the equation in my video “Is there gravity in Space?”. You then use Newton’s second law of motion to calculate the acceleration.

5. Subhobrata Chakravorti says:

Professor Mac I did not understand still why earth is accelereting upward to met a person

• Mac says:

Hi Subhobrata, there is a force between you and the Earth. That means the Earth has a force pulling on it. If it has a force on it then it will move. The thing to understand is that the force between you is a result of your mass and the Earth’s mass. You don’t need to pull on the Earth. The force is there as a natural consequence of you and Earth having mass.

6. Perfo says:

I thought i should add a bit. What prof states is totally true in terms of force’s applied not actual movement. People are jumping all around the earth, lorries elevators etc etc are all moving plus other factors. So even if you could measure how the earth moves towards you, you wouldn’t actually see it. The force you apply will be there but is only one of many. Many of which are several times larger
than the force you exert on the earth, unlike ike the force the earth exerts to you.

• Jim says:

Cool Thanks Bud. 🙂

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