# Elliptical Orbits (Using Newton's Model)

1. Jul 2, 2011

### stevmg

1) Is it theoretically possible in a universe of two planetary objects - a Sun in a fixed position and a planet of any other finite mass, for that planet to orbit the sun in a perfectly circular orbit (not an ellipse?)

2) Are the elliptical (or near elliptical) orbits that occur in the real world due to the perturbations of forces exerted on the planet which throw it "off" a perfect circle and once an imbalance is created the new balance is an ellipse?

3) Is the precession of the perihelion and aphelion of mercury about the Sun due to the increased mass of mercury (old term "relativistic mass") as it increases in velocity as it approaches its perihelion and thus forces the center of gravity or center of mass of the combined objects of the Sun and mercury to shift outward and thus force an almost imperceptible but present movement of the mercury-Sun dyad outward and thus the orbit to migrate?

2. Jul 2, 2011

### phyzguy

Yes. If the initial conditions are just right, the orbit will be a perfect circle.

No. It is not a matter of perturbations of the force law, it is a matter of initial conditions. Both circular and elliptical orbits are valid solutions of Newton's laws, it just depends on the position and velocity with which the planet starts - the initial conditions.

No, I don't think this is the correct explanation for the precession of the perihelion. It has to do with a deviation form an exact inverse square force law which is introduced by general relativity. Even a test particle of vanishingly small mass will exhibit the precession.

3. Jul 2, 2011

### stevmg

Originally Posted by stevmg
2) Are the elliptical (or near elliptical) orbits that occur in the real world due to the perturbations of forces exerted on the planet which throw it "off" a perfect circle and once an imbalance is created the new balance is an ellipse?

No. It is not a matter of perturbations of the force law, it is a matter of initial conditions. Both circular and elliptical orbits are valid solutions of Newton's laws, it just depends on the position and velocity with which the planet starts - the initial conditions.

I see and by mere real world probability it would be virtually impossible for the "perfect conditions" to exist at the initiation of a planetary orbit to send it into a perfect circle. We cannot even do that with the satellites we launch.

3) Is the precession of the perihelion and aphelion of mercury about the Sun due to the increased mass of mercury (old term "relativistic mass") as it increases in velocity as it approaches its perihelion and thus forces the center of gravity or center of mass of the combined objects of the Sun and Mercury to shift outward and thus force an almost imperceptible but present movement of the Mercury-Sun dyad outward and thus the orbit to migrate?

No, I don't think this is the correct explanation for the precession of the perihelion. It has to do with a deviation form an exact inverse square force law which is introduced by general relativity. Even a test particle of vanishingly small mass will exhibit the precession.

Yes, I know that Einstein and Hilbert used what was later termed general relativity to explain the precession but I was trying to put it into a visual image that I could understand. That may not be possible. The interesting question about the "test particle of vanishingly small mass" might be: Is the precession as much as it would be as with a planet. If, say, Jupiter were the planet in in the "Mercury orbit" (so-to-speak), would the precession be greater than it is with Mercury?

4. Jul 2, 2011

5. Jul 2, 2011

### stevmg

Anyone want to comment on this? Would a larger planet like Jupiter in the same "orbit" as Mercury have a greater precession of the perihelion-aphelion than Mercury does?

P.S.

How do you use "Multiquote?"

6. Jul 5, 2011

### BobG

It's theoretically possible to get a circular orbit if the two objects are perfectly spherical. That would be extremely unlikely, especially for rotating objects (the mass tends to shift towards the equator).

In other words, there's two reasons for no circular orbit. An incredibly low probability of initial conditions being correct is one good one. But even if the initial conditions were met, the orbital perturbations would make its "mean" orbit elliptical. (Perturbations also mean an elliptical orbit may appear "circular" for some given instant.)

7. Jul 5, 2011

### stevmg

How about Jupiter instead of Mercury in Mercury's orbit. Wouild the precession go faster? After all, the shift of the center of gravity would be more than with mercury.