# Why most of the planetary orbits are ellipitical?

1. Nov 14, 2007

### hongkongrubbish

theoretically by GMm/r^2 = mv^2/r, planets in a particular distance to the star will move in the corresponding velocity in order to maintain a circular orbit...
either over speed they will pass by the star, or under speed they will be attracted towards the star in a spiral way

So why are there elliptical orbits?

Last edited: Nov 14, 2007
2. Nov 14, 2007

### mgb_phys

Circular is just a perfect case of eliptical.
In natue there is no such thing as a circle it only exists in mathermatics. Measured in enough detail, all circles will be slightly eliptical to some degree.
Planetary orbits are almost circular, the earth's is only about 4% eliptical.

It is due to the effects of all the other planets both now and when the orbits were first forming.

3. Nov 14, 2007

### Janus

Staff Emeritus
If a planet in a circular orbit increases its speed, it begins to climb away from the star. As it does so, it loses kinetic energy to make up for the gravitational potential it gains, and loses speed. At some point, v becomes small enough that GMm/r^2 > mv^2/r, and the planet begins to fall back in towards the star gaining velocity again. It eventually gains enough speed that GMm/r^2 < m^2/r and it starts climbing back out again(this will happen at its orginal distance from the star) till it reaches the distance where it starting falling in, and repeats the cycle. IOW, it enters a elliptical orbit with its starting distance as the periapis. The only way it will leave the star is if its velocity increase to 141.4% of that needed to maintain the circular orbit at its given distance. This is known as the escape velocity.

If the planet loses speed, The reverse happens. It starts to fall in until it picks up enough speed to fling it back outward and when it reaches its orginal distance it starts to fall back in again. It enters an elliptical orbit with the original distance as the apoapis. It will not "spiral in". Only if it loses enough velocity such that the new periapis falls below the surface of the star will it hit the star. Using the Earth as an example, this would require the Earth to lose nearly all of its 30 km/sec orbital velocity.

4. Nov 16, 2007

### BrainTeaser48

Not only does the Sun's gravity effect the trajectory of the planets, but the reverse is true as well. The Sun wobbles with the gravitational infuence of the planets. And as a result of this non-uniform rotation about a "central" solar-system gravitational axis, planetary motion about the Sun has been perturbed, thus an eliptical orbit. I believe the eliptical orbits follow the shift of the Sun's orbit like the tides on Earth follow the influence of Luna. Exagerated versions of this effect have led to the discovery of high mass planets circling other stars, because those stars act like binary systems in their degree of wobble and highly exagerated eliptical orbits (determined by shadow phase observations).

5. Nov 16, 2007

### hongkongrubbish

Thank you all !! :)
So in conclusion the elliptical orbits are the results of combined gravitational forces from other planets and stars. Does it mean that the orbits are actually changing their shapes with time?

6. Nov 16, 2007

### mgb_phys

For small enough values of 'change' yes. Although the inertia of a planet is pretty large so they tend to move pretty regularly.
Planets orbits are presumably stable over long periods ( we are still here !) but proving that is one of the famous (semi) unsolved problems in maths.

7. Nov 18, 2007

### BrainTeaser48

Yes, Our star the Sun has a distinct vibration associated with the effects of planetary forces which has been measured.

8. Nov 28, 2007

### natski

Some orbits can change their eccentricity dramatially over time but remain stable due to the Kozai mechanism, where inclination and eccentricity swap over for each other.

9. Oct 28, 2009

### Visualedtech

There is a simple explanation. The sun is in motion. It is not static in the universe.
The Earth revolves around a moving object. Hence an elliptical orbit.
No Math required on this one.

10. Oct 28, 2009

### qraal

Well... no. You're wrong on the explanation. It's all implicit in the mathematics of a radial force-law and comes out rather nicely. Geometry is involved in the shape of the possible orbits - circles, ellipses, parabolas and hyperbolas - which shows they're all related curves.

The motion of the Sun due to perturbations by the planets, other stars, even the Galaxy, makes the orbits wobble around else they'd always orbit in flat planes. Instead, over aeons, they fill - approximately - a volume which defines their possible range of variation.

11. Oct 28, 2009

### Staff: Mentor

Just to clarify there - it doesn't matter if the sun is in motion or considered stationary. Either way, all orbits are elliptical (even if some of them are circular!).

12. Oct 28, 2009

### DaveC426913

It also doesn't matter whether - as mgb_phys keeps suggesting - there are or were other planets in the system. A single planet system will still be elliptical.

13. Oct 28, 2009

### ideasrule

To reiterate: orbits are always elliptical; the circle is just a special case of an ellipse. An orbit can only be circular if the planet starts off at the PERFECT speed. If that speed is precisely 30 km/s and the actual speed is 30.0000000001 km/s, the orbit's going to be slightly elliptical. The chances of finding a planet at the perfect speed is 0. Add in pertubations from other planets and eccentricity actually changes over time, though not drastically.

14. Oct 29, 2009

### qraal

Parabolic and hyperbolic orbits aren't elliptical...

15. Oct 29, 2009

### DaveC426913

Parabolic and hyperbolic trajectories aren't orbits at all. So, yes, all orbits are elliptical.

16. Oct 29, 2009

### Visualedtech

Mathematics describes the real world, it does not explain it. Math is a construct of the human mind. It helps us understand the real world.

Orbital calculations are based on assumptions. If we assume that the Sun is stationary, the calculations have to include formulas incorporating the non circular orbit observations.

We appear to live in a Spiral Galaxy. Observing such a spiral formation implies motion around a central point. If the Big Bang theory is valid, then all mass is in motion, by default. Once again, that is an assumption. Considering all the energy and forces in the universe, it is hard for me to conceive that anything could stand still.

So, assuming that the Sun has a direction and a velocity and assuming that a circular orbit would occur if the Sun was stationary, then, one should be able to calculate the velocity of the Sun. That could provide a PhD. thesis if you can stand the critizism and ridicule of your peers.

I am neither a scientist nor a mathematician, Just a little curious.
"We are here to question knowledge not to worship it".
I do not know who to attribute that quote to, but it has always been stuck in my head.

What do you think?
JJC

Last edited: Oct 29, 2009
17. Oct 29, 2009

### DaveC426913

This is all factually incorrect.

Again, orbits are elliptical around stationary bodies just as they are elliptical around moving bodies. Period.

The elliptical path around a central body depends on exactly two things, no more, no less:
- the mass of the bodies
- the angular momentum of the orbiting body

18. Oct 29, 2009

### D H

Staff Emeritus
Only one formula is needed for this: Newton's law of gravitation. That orbits are conic sections (circles, ellipses, parabolae, or hyperbolae) falls right out. You seem to have the mistaken conception that orbits must be circular. That is not the case.

19. Oct 29, 2009

### ideasrule

I think you have to reread this thread. It doesn't matter if the Sun is stationary or not; planetary orbits are NOT circular.