Elliptical Orbit- Why?

[Theophrastus]

I know that this is enevitably an obvious question, however I myself have no competence in physics, and thus curiosity has compelled me to ask: Why is it that despite a relatively uniform distribution of gravitational force, due to the sun's (somewhat) spherical shape, planets' orbits are elliptical, and not spherical?

Or, in simpler terms (as I seem to have inadvertently confused myself): Why do planets have elliptical orbits?

Any thoughts? (or answers:D; those are even better!)

[insane_alien]

well, a circular orbit is one type of elliptical orbit.

 

orbits are not always circular due to the fact that you might be going a little bit faster or slower than the velocity needed for a circular orbit.

 

if you are going faster, you will increase in altitude and if you go slower, you'll drop.

 

the shape this causes in orbit is ellipses with the earth at one of the focus points.

[Kyrisch]

the shape this causes in orbit is ellipses with the sun at one of the focus points.

 

Probably a typo on his part, so just for clarification.

[insane_alien]

actually as i was typing it i was thinking of satellites orbiting the earth rather than planets.

[Sisyphus]

Two moving bodies exerting attractive forces on one another inversely proportional to the square of the distance between them (e.g., Newtonian gravity) will always follow the path of one of the conic sections: circle, ellipse, parabola, hyperbola, or straight line. Which one just depends on their initial velocities relative to the attractive force. Orbits are pretty much all ellipses, however, because the circle is a special case - it needs exactly the right initial velocity in an exactly horizontal direction. Less and its the apogee of an ellipse, more and its the perigee. A straight line occurs with no horizontal component to the velocity, a parabola is when you have the exact minimum escape velocity, and a hyperbola is anything greater than escape velocity (so not really an "orbit"). You can show this with calculus, and in fact it's pretty much the reason Isaac Newton developed calculus in the first place.

Edited July 6, 2009 by Sisyphus

[swansont]

One might argue that the straight line really isn't an orbit, either. More of a poor lifestyle choice.

[Airbrush]

well, a circular orbit is one type of elliptical orbit.

 

Well said. Generally speaking, all the planets in the solar system follow elliptical orbits around the Sun, but NEARLY circular.

[J.C.MacSwell]

One might argue that the straight line really isn't an orbit, either. More of a poor lifestyle choice.

 

One might argue the parabola and hyperbola aren't either.

 

Is straight really that bad a lifestyle choice?

 

Not that there's anything right with it!

[Severian]

Is straight really that bad a lifestyle choice?

 

Homophobe!

[swansont]

One might argue the parabola and hyperbola aren't either.

 

Is straight really that bad a lifestyle choice?

 

Not that there's anything right with it!

 

Parabola and hyperbola don't have you crashing into the gravitational partner.

[insane_alien]

Parabola and hyperbola don't have you crashing into the gravitational partner.

 

depends on if the orbit crosses the surface of the gravitational partner.

 

its quite possible to have a paraboloic/hyperbolic orbit that goes below the surface.

 

evidence: every single meteorite.

[Sisyphus]

depends on if the orbit crosses the surface of the gravitational partner.

 

its quite possible to have a paraboloic/hyperbolic orbit that goes below the surface.

 

evidence: every single meteorite.

 

Or just tossing a ball (ignoring air resistance). On small scales, you can assume that the gravitational field is uniform and parallel and thus trajectories will be parabolic. Really, though, the path of the ball is the portion near the apogee of an extremely eccentric ellipse that just barely emerges from the surface. Collapse the rest of the Earth into a point mass while the ball is in mid air, and it will continue to follow the same path, but instead of intersecting with the surface will continue orbiting, swinging very close to the center of gravity while moving extremely fast, return to where you threw it from, and go around again indefinitely.

[insane_alien]

i was talking about a parabolic orbit where the object is travelling at escape velocity at the periapsis.

[Sisyphus]

i was talking about a parabolic orbit where the object is travelling at escape velocity at the periapsis.

 

I know. I was just adding that any "orbit" can intersect the surface, and that in fact we witness this all the time in everyday experience, for anything in free fall. But in everyday experience, it's basically always an ellipse, as we don't typically encounter objects moving at escape velocity or faster.

 

(As always, of course, all of this only applies to a classical approximation.)

[swansont]

depends on if the orbit crosses the surface of the gravitational partner.

 

its quite possible to have a paraboloic/hyperbolic orbit that goes below the surface.

 

evidence: every single meteorite.

 

I should have been more clear: those other orbits may intersect, but a linear orbit must intersect. Unless your gravitational partner is a torus, you get (at most) one half of a period of "orbit" before smackdown time.