# If someone were in a vacuum, and the only things inside were a person and a ball, would the ball be pulled toward the person with gravity?

Just a silly question I was thinking about since if gravity is the force acting between physical bodies with mass to bring them together, then wouldn't the ball be pulled toward the person, (of course with the person also being slightly pulled towards the ball). If so, wouldn't this be like the "force" from Star Wars?

Ye, the ball and the person would attract each other, but the force between them would be so small it hard even to measure it. As a way of defeating Sith Lords it would leave a lot to be desired.

$$F = \frac{Gm_1 m_2}{d^2}$$

where $m_1$ and $m_2$ are the masses of the two objects, $d$ is the distance between them and $G$ is a constant called the gravitational constant. Suppose the ball weighs $150$g (the weight of a baseball), and it's $2$m away from me (weight $66$kg). The force between me and the ball would be:

$$F = \frac{G \cdot 0.15 \cdot 66}{2 \cdot 2} \approx 0.17 \,\text{nN}$$

where $\mathrm{nN}$ means a nano-Newton. If I waited a year the ball would have accelerated to a massive speed of $3.4$ cm/sec.

Gravitational force would still be far far less for such a less mass as that of a human being. So no, it would be so less to actually see something significant.

The force of gravitational on a body is given by $$F = G \frac {m_1 m_2}{r^2}$$

The value of $G$ is $6.67 × 10^{-11} m^3 /kg \, s^2$.

As a result, the gravitational force between two humans, or even two very big engineering cranes, is very less, though it is always present. That said, you can realise that the force of gravity between a ball and a man will be of the order of $10^{-11}$, as a result of which none would move towards each other, even in vaccum.

I assume that when you say vacuum you are intending to say that the two objects are far enough away from anything else so that gravity from all other objects is negligible.

The force of attraction between two bodies is given by the equation $$F_{grav}=\frac{GM_1M_2}{r^2}$$where G is the gravitational constant, $6.67\times 10^{-11}$, $r$ is the radius and $M_1$ and $M_2$ are the masses of the two objects. So, yes, there will be a force of gravity between them and they will slowly be attracted to each other. Now, the time it takes for two objects to attract each other due to the force of gravity is given by $$t = \pi\sqrt{\frac{r_0^3}{8G(m_1+m_2)}}$$So in fact for two objects of mass $1kg$ and $70kg$ $($about that of a human$)$ with an initial radius, $r_0 = 1m$, the time it takes is approximately $16,000$ seconds, which isn't actually too long at all, however for it to be of a similar time of the force in star-wars the person would have to be very massive $($unrealistically so$)$.

## protected by Qmechanic♦Oct 1 '17 at 14:49

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