# The Naked Scientists Forum

### Author Topic: When does escape become orbital?  (Read 1046 times)

#### jeffreyH

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##### When does escape become orbital?
« on: 28/08/2015 15:23:41 »
If we have an object moving away from a source at a velocity that is less than the escape velocity by an infinitesimally small amount can we say it is describing an orbit? Then can we describe an infinitesimally small decrease in the velocity that would not describe an orbit? I am assuming that the object moving away from the source is not exactly perpendicular to the surface of that source.

#### evan_au

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##### Re: When does escape become orbital?
« Reply #1 on: 30/08/2015 01:05:08 »
An object in orbit follows an elliptical path (a circular orbit is just a special case of an elliptical orbit).

When a satellite approaches escape velocity, the ellipse becomes very "stretched": long and skinny (high eccentricity).

At the farthest point in the orbit, the satellite is moving most slowly. So, just below escape velocity, the satellite would be almost stationary, and could spend millions of years far from the Sun. You would need to measure it's velocity very carefully to see if it would fall back in towards the Sun in an elliptical orbit, or if it would drift on "to infinity".

If the satellite escapes to infinity, it is not called an orbit, because it is no longer a closed path.
If the satellite has exactly escape velocity, it's path will follow (part of) a parabola.
If the satellite has more than escape velocity, it's path will follow a hyperbola.

The escape velocity is usually measured from ground level - if an object already in orbit is then accelerated to just below escape velocity (for the ground), then it will escape to infinity. Such an path is an hyperbola.

Circles, Ellipses, Parabolas & Hyperbolas are all conic sections, and there is a very small velocity separating an elongated ellipse (eccentricity→∞) from a parabola or a hyperbola.
« Last Edit: 30/08/2015 04:03:21 by evan_au »

#### jeffreyH

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##### Re: When does escape become orbital?
« Reply #2 on: 30/08/2015 11:03:17 »
The next question is can this be formulated as a probability in the quantum mechanical sense.

#### The Naked Scientists Forum

##### Re: When does escape become orbital?
« Reply #2 on: 30/08/2015 11:03:17 »