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stitt29
2009-Aug-22, 02:39 PM
Hi

if we have an object in deep space with no gravitational pull from anything. And this object fires a cannonball into orbit i.e. not fast enough for escape velocity but fast enough to go into an elliptical orbit. lets say the cannonball is 1/1000th the mass of the object. so the cannonball will set off at 1000xm/hour and the object at xm/hour in the opposite direction. does the fact that the largest mass is moving away from the cannonball have any bearing on the orbit?

would the aphehelion be further away than if the larger object wasn't moving? and also would the perihelion be closer. Does this make the orbit longer or shorter? does the shortening or lengthening continue? i.e. do the objects eventually collapse into each other or do the drift apart?

matthewota
2009-Aug-22, 03:06 PM
Your question is very confusing, because you first define an object in space with no gravitational influences. Then how can you fire something into orbit around anything? You stated the conditions of no gravitational influence, so there is nothing for the object to orbit.

Jeff Root
2009-Aug-22, 09:05 PM
Clearly stitt29 intends that the mutual gravitational attraction between
the "cannonball" and the "object" causes them to orbit one another.

stitt29,

If the cannonball moves directly away from the more massive object at
less than escape speed, it will reach a maximum distance and then begin
to fall straight back to its launching point. However, if you give the
cannonball a little sideways push anytime after it has been launched,
it will go into orbit.

When two bodies are involved, and one is far more massive than the other,
it is convenient to say that the less massive body orbits the more massive
body. When the two bodies are nearly the same mass, it is convenient to
say that they orbit each other. In all cases, nomatter what their masses,
they each orbit their common center of mass, or barycenter.

You can imagine the barycenter as a fixed point around which the two
bodies orbit. There actually is no such thing as "a point in space", whether
fixed or moving, but for purposes of analyzing motion, there is nothing wrong
with visualizing the orbits as being around an imaginary fixed point in space.
This imaginary "fixed point" can be moving at any speed in any direction
relative to anything or everything else in the Universe. That is completely
irrelevant.

If the massive object is 1000 times the mass of the cannonball, the radius
of the cannonball's orbit will be 1000 times the radius of the object's orbit.
The two orbits will be the same shape. That is, if the cannonball is in an
elliptical orbit with an eccentricity of 0.8, then the more massive object
will also be in an elliptical orbit with an eccentricity of 0.8. It will just be
a smaller ellipse.

It makes no difference whether the cannonball accelerates away from the
more massive object or the more massive object accelerates away from
the cannonball. All you are doing is moving them apart so that they are
not in contact, permitting them to orbit each other. Motions relative to
the rest of the Universe are irrelevant. There is no difference between
the cannonball moving away from the object, and the object moving away
from the cannonball. They are just one motion: The cannoball and the
object moving away from each other. So most of your questions don't
have any meaning. It is like asking what the difference is between 2 x 3
and 3 x 2. There can't be a difference because they're the same thing.

In the absence of other forces, the object and cannonball will continue
to orbit their common barycenter forever.

-- Jeff, in Minneapolis