Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass and thus attracts everything else. If a book was accelerated to the center of mass of the whole rocket + everything in it, why would it not stay there instead of floating back and forth like they show in movies? Does this have to do with how weak the gravity is, so when it falls it's actually not enough force to keep it from bouncing back like on planets? Thanks

The rocket is in free fall along with the book. The nearest gravitating bodies are very far away, so whatever meager acceleration they cause will be almost exactly the same on the rocket and on the book.

Suppose you instead went on a very close flyby of a neutron star. Now the book will fall rapidly, and away from the rocket's center of mass. The only way to avoid this is to have the book exactly at rest with respect to the rocket and exactly at the rocket's center of mass.

The difference between the first and second scenarios is called "tidal gravity". There is so little gravity gradient in the first scenario that it will never be observable. In the second, I specifically chose a setting where tidal effects are very large, larger than predicted by Newtonian mechanics.

Suppose we choose an in-between scenario, say a flyby of an asteroid. There will still be tidal effects, much reduced from those of the neutron star but much increased compared to empty space. Here the predictions from Newtonian mechanics will be more or less correct.

The forces involved can be calculated with the following equation: $$F = \frac{GMm}{d^2}$$

A fueled Saturn V was about $3.0 \times 10^6 kg$. Most of it doesn't reach space but we'll be conservative and say your spaceship is that massive. If you had a 1kg book that could somehow be only 1 meter away from the entire mass, what would be the gravitational force?

$$F = \frac{G (3.0\times 10^6kg) (1kg)} {(1m)^2}$$ $$F = (6.67 \times 10^{-11} \frac{m}{kg s^2}) (3.0 \times 10^6 kg^2)$$ $$F = 2.0 \times 10^{-4} N$$

Ordinary forces on the book (touching, airflow, etc.) will overwhelm this tiny force. You'd never notice. In practice, the effect will be much less. The fact that the spacecraft mass surrounds the cabin rather than pulls in a single direction will reduce the effect further.

Your question is actually quite a complicated one as there are lots of different factors at play. However if you're asking why the objects inside the rocket don't attract each other then the main reason is that gravity is actually a very weak force. If a book is floating a metre away from me then the gravitational acceleration of the book due to my mass (70kg) is given by:

$$a = \frac{GM}{r^2} \approx 5 \times 10^{-9} \text{m/s}^2$$

So you'd waiting an awfully long time for the book to move towards me. In practice of course random air currents would completely swamp the attraction between me and the book.

Some objects in orbit can be startlingly heavy. For example the International Space Station has a total weight of about 450,000 kg. But there are two reasons why this doesn't have much effect on the objects inside it:

1. although it's heavy the ISS is big, so the mass is spread out over relatively large distances

2. most of the mass is in the walls, and the astronauts are inside the walls

Reason (2) is one of those complications I alluded to earlier. In your question you say:

If a book was accelerated to the center of mass of the whole rocket

But this isn't what happens. Objects are not accelerated towards the centre of mass. In fact if you're inside a spherical shell of matter (e.g. a spherical spacecraft) then the gravity inside cancels out and is exactly zero. This principle even has a name - it's called the shell theorem.

Real spacecraft are unlikely to be spherical, but the basic principle still applies. If you're inside the spaceship the walls of the ship pull at you from all directions and tend to cancel each other out. The centre of mass is actually likely to be a point where the net gravity is very low.

The remaining point is dealt with in David's answer. There actually isn't anywhere in the universe where there is no gravity because the entire universe is evolving in response to the combined gravitational fields of all the matter in it. Actually its evolution is currently dominated by the dark energy in it rather than the matter in it, but let's gloss over that. Anyhow, once the rocket motor is off the rocket and everything in it feel the same external gravity so they don't move relative to each other. That's why the astronauts in the ISS are weghtless even though the ISS is well within Earth's gravitational field.

Well, this isn't quite true. The Earth's gravitational field varies with distance, so it's slightly stronger at the side of the ISS nearest the Earth than it is at the side of the ISS farthest away from the Earth. This creates a tidal force, and actually to the people in the ISS this looks like a repulsion. If we go back to me and the book, if the book is nearer the Earth than me it will accelerate towards the earth faster than I will, and I and the book will move apart. To me it looks as if I and the book are repelling each other not attracting each other.

The tidal acceleration between two points separated by a small distance $\ell$ at a radius $r$ from the Earth is:

$$a_t = \ell \frac{2GM}{r^3}$$

and if we feed in the mass of the Earth, and the distance of the ISS from the Earth we get:

$$a_t \approx 2.6 \times 10^{-6} \text{m/s}^2$$

So the tidal force between me and the book is pulling us apart about 500 times more strongly than our mutual gravity is pulling us together.

However this only happens because the Earth is quite nearby. If you went off into deep space the tidal forces would be negligable.

This is because in deep space everything is being attracted equally in all directions since the universe is homogeneous. Hence, all of these tiny gravitational forces acting on the objects in your ship cancel out. Therefore you are left with a net force equal to zero on these objects in your spacecraft.

On reflection, forget deep space for the time being and just consider yourself aboard a satellite orbiting the earth. Like you see in the movies everything just floats as if no net forces act on them. This is not true though. The mass of the earth is attracting each object towards the earth.

So basically all the objects aboard the satellite (including the satellite itself) are 'falling' towards the earth. If everything is accelerating toward the earth including you, the craft and its contents then you are effectively moving with the objects and the craft

But if everything is moving at once (albeit very, very slowly). Then how could you possibly make observations on individual objects like say a book on the craft?

• You would have to be in intergalactic space for this to be the case. I doubt that Joe is looking for a case as special as that. – HDE 226868 Aug 28 '14 at 18:23
• @HDE226868 Yes that's true but OP did say deep space, all i'm trying to say is that however weak the gravitational forces may be the objects within the ship are being pulled in all directions at the same time. This could be due to gravity from stars/planets or the ship itself. – BLAZE Aug 28 '14 at 18:29
• I disagree with the statement that large-scale homogeneity implies gravitational equilibrium. Some objects will have more influence than others because they are nearer. – HDE 226868 Aug 28 '14 at 18:36