# Why don't heavenly bodies attract each other stronger? [duplicate]

In my physics textbook, it's written that

According to the laws of gravitation force,

• all masses attract each other
• the greater the masses, the stronger the pull
• the closer the masses, the stronger the pull

The pull between small masses is far too weak to measure. But the earth has such a huge mass that its gravitation force is strong enough to hold most things firmly on the ground.

The attraction between me and the earth is strong. Since the force exerted by the Earth is much more stronger than the force I exert on earth, I'm pulled towards it.

Now the attraction between heavenly bodies, let's say the earth and the moon, should be stronger than the attraction between me and the earth. At least according to the second bullet point on gravitation force. The earth should literally stick to the moon even more strongly than it will stick to me. Fat people tend to feel a stronger pull force from the earth.

The attraction between the earth and the moon is not weak, nevertheless. But why isn't it as strong as it should be?

## marked as duplicate by WillO, Yashas, Qmechanic♦May 15 '17 at 9:04

• Think again , the force exerted by you on earth and by earth on you is same , from Newtons 3rd law. – Physicsapproval May 15 '17 at 6:09
• For second part, physics.stackexchange.com/q/9049 – Physicsapproval May 15 '17 at 6:16
• Maths is your friend here, and the inverse square law of Newton's Universal Law of Gravitation. – HsMjstyMstdn May 15 '17 at 6:22
• Have you learned about orbits? Just because two bodies attract each other strongly, that does not mean they will "stick" to each other. In fact, two bodies can be very strong attracting but never touch each other. – DanielSank May 15 '17 at 6:43
• Down-voting because of your comment: "Why do orbits even happen". You don't seem to have an understanding of what you're asking. – Kunal Pawar May 15 '17 at 7:09

Since the force exerted by the Earth is much more stronger than the force I exert on earth, I'm pulled towards it.

Actually, the forces are the same. Newton's 3rd law says so: $$\vec F_{\text{A on B}}=-\vec F_\text{B on A}$$ The pull from Earth in you equals your pull in Earth.

But different masses respond to a force differently. This is Newton's 2nd law:

$$\sum F=ma$$

The same force causes less acceleration of a body that is much more massive.

Now the attraction between heavenly bodies, let's say the earth and the moon, should be stronger than the attraction between me and the earth. At least according to the second bullet point on gravitation force.

Well, the second bullet point says that the mass plays a role. You are much less massive than the Moon. So that factor is not in your favour. But you are much closer. That factor is in your favour. Which factor counts most is found by calculating the actual force with the formula for gravitational force, Newton's law of gravity:

$$F=G\frac{m_1m_2}{r^2}$$

We can try to plug in numbers and see if you or the Moon experiences largest force. The gravitational constant is $G=6.67\times 10^{-11}\;\mathrm{N\;m^2/kg^2}$ and Earth's mass $m_1=5.97\times 10^{24}\;\mathrm{kg}$. The Moon's mass is $m_{2,\text{Moon}}=7.35\times 10^{22}\;\mathrm{kg}$ and it is $r_{\text{Moon}}=384\;400\;\mathrm{km}$ from Earth (average distance from centre to centre) and your mass around $m_{2,\text{you}}=70\;\mathrm{kg}$ and your distance is $r_{\text{you}}=6400\;\mathrm{km}$ (from centre to you; Earth's radius):

$$F_{\text{between Earth and you}}=G\frac{m_1\;m_{2,\text{you}}}{r^2}=681\;\mathrm N\\ F_{\text{between Earth and Moon}}=G\frac{m_1\;m_{2,\text{Moon}}}{r^2}=1.98\times 10^{20}\;\mathrm N$$

We see here that the Moon is being pulled in very much more than we are being pulled in. So you are indeed right that the very large masses here have the biggest influence.

The earth should literally stick to the moon even more strongly than it will stick to me.

If it wasn't moving, then yes, it would fall towards earth and crash into us. What exactly do you mean by "sticking"? Since the Moon is moving sideways over the sky, it is not reaching Earth but always constantly flyign "around" Earth; it is falling towards Earth but "missing", so to speak. They never come in contact.

But seen from a distant planet, one might say that the Moon is stuck in the orbit around Earth, yes. But if it is strongly stuck or weakly stuck depends a lot on what you mean - if you pull it away from Earth, then yes, you must overcome Earth's gravitational pull in order to move it. If you pull along with it's direction, then it is a direction in which Earth's gravity has no influence.

Fat people tend to feel a stronger pull force from the earth.

If "fat" means "more massive" then true.

But why isn't it as strong as it should be

Should it be something specific, or what do you mean? The current attraction between Earth and Moon seems just fine to me, making the moon spin around Earth with one round a month. What do you mean with this question?

While the force between the Earth and the Moon is much stronger, around 2e20 N, there is one big difference between the Moon and you. The moon is in orbit around Earth. Otherwise, the Moon would indeed stick to the Earth.