If gravity is in all things, why doesn't my pen orbit my burrito?

Question

I know I know. The earth's gravity overrides the theorized attraction of these two items. Consider then, that the conditions were perfect. We set two small items- say, lead sinkers of relative, scale mass and distance of the earth and the moon, in deep space- hundreds of lightyears away from any gravitational interfearance. We then start these objects spinning in a perfect orbit. Do the objects continue to orbit each other? Or do they drift apart? If, by chance, the objects do not attract each other, how is it that atoms and molecules hold together in the same circumstances?

I'm pretty amazed with the amount of time you fellows have put into your answers. Thanks a lot. Of course you know how it goes- more answers mean more questions.

Math can prove anything, provided we know what the rules are. Problem is, most of the rules envolving gravity are all theory. We still can't say for sure what gravity is and what causes it. My next question would be: Has this experiment been done before? Have we found evidence showing non-magnetic attraction between two small objects?

Answer 1

1) You do not have to be too far from Earth to observe this. However, you need to have all objects involved to be falling at the same rate in the outer gravitational field. Then the tiny gravitation fileds of the burrito and your pen will interact with each other and they will both orbit their common centre of gravity.

2) Of course, if you are observing this from relatively close by, your own gravitational field may affect them. If you are very far (compared to their distance from each other), then the pair will orbit you. If you are too close, you will disrupt their orbit around each other and they will enter separate orbits around you.

3) Let's pretend you are not there but the pair is in free fall "relatively" near a bigger object. Let us say that you have placed you experiment in orbit around Earth at the same distance as the Moon, but not close to the Moon. The gravitational field of Earth is relatively flat at that distance, but it is not completely flat. There will be a tidal effect on the orbit of the objects around each other. When the long axis of their orbit is in line with Earth's field (i.e., long axis pointing towards Earth), the orbit will become a bit more eccentric (the ellipse becomes more "squished").

The orbit of the two objects will have to be small in order not to be disrupted by nearby Earth (even at that distance). Because you pen and you burrito have size (and I suspect you of having had your burrito "super-sized"), too much tidal effect will squish the orbital ellipses to the point where the two objects may collide (which would definitely disrupt the orbits).

3) Like any object that orbit each other, they are emitting gravitational waves, therefore the system is losing energy. However, this will take an extremely long time (billions of years) as gravitational waves do not carry a lot of energy. Astronomers are still trying to detect gravitational waves from neutron stars and black holes orbiting each other. Imagine how difficult to detect a burrito-pen wave.

Atoms in molecules are held together by forces that are much stonger than gravity. No problem there.

However, if your burrito is hot and rather liquidish inside, it may decide to spring a leak if you leave it in vacuum.

---

wdmc's approach to calculate the orbital period is OK as long as the mass of the pen is very small compared to the mass of the burrito. Such approximations are OK when we compare planetary orbits around the Sun (the mass of each planet is very small compared to the Sun).

But if the masses are relatively close to each other (even 1/10 may affect the calculations), then you have to use more detailed equations. Therefore, you better SUPER-super-size that burrito, plus extra cheese, as cheese adds mass and binding to keep everything together...

Answer 2

Newton's Law of Gravitation
F = G*(m1*m2)/r^2

F is the force between the objects
G is the gravitational constant
( http://en.wikipedia.org/wiki/Gravitational_constant )
m1 and m2 are the mass of the burrito and pen
r is the distance between them

For the pen is to remain in a circular orbit around the burrito, the pen's centripetal force must be equal to the gravitational force.

Centripetal Force:
F = (m2*v^2)/r
m2 is the mass of the pen
v is the pen's velocity
r is the distance between the pen and the burrito

Setting these equations equal, you can solve for the period of the pen's orbit and get:
T^2 = (4*pi^2)*(r^3)/(G*m1)
T is the period
m1 is the mass of the burrito
(every teacher will point out that the mass of the pen is not a determining factor in its orbital period.)

Answer 3

Thank you. You gave me my laugh for the day! Some day, along with such sayings as "Cogito, ergo sum!" ("I think, therefore I am!) and "Veni, vidi, vici!" ("I came, I saw, I conquered!), my own quotation, "Math works! Physics doesn't!"

Regarding your question, though, with what little physics I studied in college, I would think that a physicist would say is that they would continue to orbit each other unless and until they are acted upon by an outside source, (but, then again, physicists deal with massless ropes and frictionless pulleys!).

The physicists would also cite covalent bonds and other nonsense to explain how the atoms and molecules hold together. ; )

Thanks again!

Answer 4

Depending on their distance between them, and there rotation speed, they will orbit each other, but this wont work for ever, cause this movement takes engery, their Angular momentum to be specific, and so they will someday just collide, and will stick together, like most of the material in space did.

Answer 5

If they are moving slowly enough then yes they will orbit each other. The gravity is so low that the orbital period might be years. You can compute the answer.

Answer 6

They will go into and stay in a mutual orbit if the initial conditions are correct (spacing and speed).

Answer 7

The Earth gravity is so strong that it "nullifies" this.

If you are very far in outer space, particularly LaGrance points, then your pen will orbit your burrito.