<p>We can use Newton's law of gravity to calculate the force the Earth feels from the moon:</p>

<p>$$
F_g = \frac{GM_{Earth}M_{Moon}}{r^2}
$$</p>

<p>Where G is the universal gravitational constant, $6.62*10^{-11}$ $m^3 kg^{-1} s^{-2}$, $M_{Earth}$ and $M_{Moon}$ are the masses of the Earth and Moon in kilograms, and $r$ is the distance between their center s in meters.  We can rearrange this equation to solve for a distance like so:</p>

<p>$$
r = \sqrt{\frac{GM_{Earth}M_{Moon}}{F_g}}
$$</p>

<p>Now we can input any force we like to see how far away the Moon would have to be in order for us to feel that force.  If we want the force of gravity to go to zero, we can take the limit as $F_g\rightarrow 0$.  When we do this, we see that for the Earth to feel zero gravitational force from the Moon, it would have to be infinitely far away.</p>

<p>However, infinity is not a very useful number; why don't we look for something a little more practical?  Let's say that we want the Earth to feel exactly 0.01 Newton of gravitational force from the Moon.  That's about the weight of 1 gram of matter at the Earth's surface.  In that case, we will have $r=5.411*10^{19}$ meters or $3.4*10^{14}$ miles, about $1.4*10^{11}$ times further away.</p>

<p>Keep in mind, though, that this is still not zero force.  It's small enough that we probably wouldn't be able to detect it, but it is nonzero.</p>

CC BY-SA 3.0
2017-03-20T04:16:28.560Z
What about a distance where Earth would start spinning violently on its axis?
Joe
CC BY-SA 3.0
2017-03-20T04:23:25.843Z
I am actually doing this for science extra credit. My teacher said that we would die if the moon got too far away. He wants us to figure out when this will happen.
Joe
CC BY-SA 3.0
2017-03-20T04:26:43.110Z
Now that's a lot more complicated.  If you do some basic research online, you should be able to find estimates though.
Phiteros
CC BY-SA 3.0
2017-03-20T04:27:52.573Z
Can you help? I tried and could't find anything.
Joe
CC BY-SA 3.0
2017-03-20T04:38:32.383Z
[This Wikipedia article](https://en.wikipedia.org/wiki/Orbit_of_the_Moon#Tidal_evolution) should answer some of your questions.
Phiteros
CC BY-SA 3.0
2017-03-20T04:13:12.550Z
2017-03-20T04:13:12.550Z
Phiteros
<p>How far in miles does the Moon have to be for the Earth not to feel its effects?</p>

CC BY-SA 3.0
2017-03-20T03:57:42.287Z
Technically, the answer would be "infinity".  On a more practical level, the moon will always have some gravitational effect on the Earth, no matter how far away it is.  The real question is how small you want those effects to be.
Phiteros
CC BY-SA 3.0
2017-03-20T03:59:49.530Z
I don't believe that to be true. There is a distance where the moon will have no effect on the Earth in the sense of gravitational effects. I need an actually number please.
Joe
CC BY-SA 3.0
2017-03-20T04:13:58.917Z
It doesn't matter what you believe to be true.  What matters is what the math says.  And the math says that you would need to be infinitely far away to feel zero force.
Phiteros
CC BY-SA 3.0
2017-03-20T07:21:39.110Z
Joe, the force of gravity drops as $1/r^2$, and so never goes to zero. But if you want to pick a specific effect, for example tidal force, you can ask how far the moon has to be to drop by half, or 90%. I can't guarantee the answer will be simple, but right now your question's answer is really "infinity" as @Phiteros says.
uhoh
CC BY-SA 3.0
2017-03-20T16:50:26.923Z
Please stop posting the same question over and over and over.
HDE 226868
<the-moon><earth>
How far away does the Moon have to be until Earth doesn't feel its effects?
Joe
# How far away does the Moon have to be until Earth doesn't feel its effects?

(Asked by: username_0 on 2017-03-20)

How far in miles does the Moon have to be for the Earth not to feel its effects?

**Tags:** the-moon, earth
> **Comments:**
> **username_1**: Technically, the answer would be "infinity".  On a more practical level, the moon will always have some gravitational effect on the Earth, no matter how far away it is.  The real question is how small you want those effects to be.  
> **username_0**: I don't believe that to be true. There is a distance where the moon will have no effect on the Earth in the sense of gravitational effects. I need an actually number please.  
> **username_1**: It doesn't matter what you believe to be true.  What matters is what the math says.  And the math says that you would need to be infinitely far away to feel zero force.  
> **username_2**: Joe, the force of gravity drops as $1/r^2$, and so never goes to zero. But if you want to pick a specific effect, for example tidal force, you can ask how far the moon has to be to drop by half, or 90%. I can't guarantee the answer will be simple, but right now your question's answer is really "infinity" as @Phiteros says.  
> **username_3**: Please stop posting the same question over and over and over.  

---

## 1 answers

### Answer by username_1 on 2017-03-20. Score: 2 | Accepted answer

We can use Newton's law of gravity to calculate the force the Earth feels from the moon:

$$
F\_g = \frac{GM\_{Earth}M\_{Moon}}{r^2}
$$

Where G is the universal gravitational constant, $6.62\*10^{-11}$ $m^3 kg^{-1} s^{-2}$, $M\_{Earth}$ and $M\_{Moon}$ are the masses of the Earth and Moon in kilograms, and $r$ is the distance between their center s in meters. We can rearrange this equation to solve for a distance like so:

$$
r = \sqrt{\frac{GM\_{Earth}M\_{Moon}}{F\_g}}
$$

Now we can input any force we like to see how far away the Moon would have to be in order for us to feel that force. If we want the force of gravity to go to zero, we can take the limit as $F\_g\rightarrow 0$. When we do this, we see that for the Earth to feel zero gravitational force from the Moon, it would have to be infinitely far away.

However, infinity is not a very useful number; why don't we look for something a little more practical? Let's say that we want the Earth to feel exactly 0.01 Newton of gravitational force from the Moon. That's about the weight of 1 gram of matter at the Earth's surface. In that case, we will have $r=5.411\*10^{19}$ meters or $3.4\*10^{14}$ miles, about $1.4\*10^{11}$ times further away.

Keep in mind, though, that this is still not zero force. It's small enough that we probably wouldn't be able to detect it, but it is nonzero.

> **Comments:**
> **username_0**: What about a distance where Earth would start spinning violently on its axis?  
> **username_0**: I am actually doing this for science extra credit. My teacher said that we would die if the moon got too far away. He wants us to figure out when this will happen.  
> **username_1**: Now that's a lot more complicated.  If you do some basic research online, you should be able to find estimates though.  
> **username_0**: Can you help? I tried and could't find anything.  
> **username_1**: [This Wikipedia article](https://en.wikipedia.org/wiki/Orbit_of_the_Moon#Tidal_evolution) should answer some of your questions.  

---

