Where to find zero gravity far from a planet?

suppose we have such a planet which nothing is around it(you can say it's alone in the universe) . I want to know where we can find a point that we didn't feel the gravity force of planet. if you have article or formulas about it I appreciate your help.

• If your planet of interest happened to be a shell, you'll have zero gravity inside the shell. – Yashas Jun 30 '17 at 4:26
• If you went to that spot, how would you know you found it? How would you feel it? You'd have to "feel" it somehow, perhaps by measuring tidal forces. But every measuring device has a limit to how small an effect it can detect. So examine your measuring device, find it's limit of sensitivity, and then go as far away from the planet as you need for the tidal force (or whatever you are measuring) to be below the limit of sensitivity. At that point you have found a point that we didn't feel the gravity force of the planet. – garyp Jun 30 '17 at 11:25

By Gauss's law for gravity, $$\oint_S \mathbf{g} \cdot \mathrm{d\mathbf{S}} = -4\pi GM$$ You seem to be looking for a point where the net gravitational flux is zero. This would happen only in a surface enclosing no mass!

For example, a shell. Or the example @Hritik has provided, a cavity in a sphere, where at any point in the cavity, the force would be zero. (No mass is enclosed by the cavity)

You can't. The gravitational influence of the planet extends to infinity. Though technically the center of the planet is a zero-gravity point, ordinarily there's already stuff there. Specifically, the gravitational acceleration an object experiences a distance $r$ from the center of a planet is

$a=\frac{GM}{r^2}$,

as long as you're outside the planet.

• is there a formulas that represent the value of the gravity in the every point of space(if we say that the planet is spherical) – user152372 Jun 30 '17 at 3:27
• Edited to include formula. – probably_someone Jun 30 '17 at 3:29
• Unless the planet is a shell ;) – Yashas Jun 30 '17 at 4:26
• The formula is still valid everywhere outside the shell, or the planet. Only at infinity do we say you can have an observer that feels no force. Same is true in General Relativity. – Bob Bee Jun 30 '17 at 4:35

If you have a uniform spherical planet, the gravitational field due to it is:

$$-\frac{GMr}{R^3} \tag{r < R}$$

$$-\frac{GM}{r^2} \tag{r \geq R}$$

There is only one point where the force can be zero, and that point interestingly is not far far away but is at $r=0$. (although there is stuff there, it technically still is a point)

Interesting fact: If you were to have a spherical cavity in the center of the planet, the force would be zero at every point inside the cavity!