Why orbits eliptical?

[photon]

Greetings, people of Earth

I was just wondering why the planets and other orbiting objects have eliptical orbits instead of circular ones.
HELP!

 

[drag]

Greetings !

It's rather simple really, an elliptical orbit is
the general case and a circuilar orbit is the specific
case. An elliptical orbit is a definition that fits any
orbit while a circuilar orbit is some specific - perfect
case. For example, imagine you take pieces of a puzzle
and drop them on the table, there's little chance - one
perfect case for them to fall in the right order to solve
the puzzle right away, however, all of them will lie on
the table somewhere.

Live long and prosper.

 

[Ambitwistor]

If you described why you think orbits ought to be circular, perhaps that would help in explaining why they aren't.

I'm not sure why you should expect them to be circular: given a centripetal force of constant magnitude F at a given radius R, you only get uniform circular motion when the velocity of the object is given by one specific value v, obeying F = mv^2/R. If the velocity has any other value, then uniform circular motion cannot be maintained.

 

[photon]

It seems they would be circular because with a spherical object such as the sun, and a spherical orbiting object such as a planet, that the orbit should be a circle. In all the pictures in books, it shows a grid, sucked down by a shere. The "pit" in the space-time grid is always shown as a circle.

 

[Phobos]

Welcome to Physics Forums, photon & Ambitwistor!

Given the cosmic demolition derby of planetary formation, plus all the chaotic gravitational nudges of a complex, dynamic solar system, maintaining a perfectly circular orbit it not easy thing for a planet to do. Small changes in velocity (e.g., due to gravitational effects or resulting from impacts with other large objects) will throw the object out of a circular orbit and into an elliptical orbit.

 

[chroot]

Originally posted by photon
It seems they would be circular because with a spherical object such as the sun, and a spherical orbiting object such as a planet, that the orbit should be a circle. In all the pictures in books, it shows a grid, sucked down by a shere. The "pit" in the space-time grid is always shown as a circle.

The Sun is not a sphere. Neither is the Earth.

- Warren

 

[Ambitwistor]

Originally posted by photon
It seems [orbits] would be circular because with a spherical object such as the sun, and a spherical orbiting object such as a planet, that the orbit should be a circle.

The gravitational field of a spherically symmetric body is spherically symmetric, but this does not imply that orbits around that body must also be spherically symmetric. (It's like claiming that if a gravitational field points straight down, all bodies should fall straight: they don't have to, they can move in parabolas.)

Imagine just dropping a body above the Earth: it won't go in a circle, it will fall straight down. Now imagine dropping it, but giving it a very small sideways kick: again it won't travel in a circle, it will fall, but not straight down: it will move in an arc (which is part of an ellipse).

 

[photon]

ah. Thanks guys, I think I get it now.

 

[NEOclassic]

Originally posted by photon
ah. Thanks guys, I think I get it now.

Hi photon and welcome to this string,

You're a real spunky and curious kid and I admire your confidence in your belief that "you have finally got it". As a math scholar and a fairly able logician, I have doubted the veracity of Kepler's first law for decades; the part about elliptic orbitals cannot be denied but the notion that the Sun is at a single elliptic focus is ridiculous. When I was in about 8th grade general science class, the teacher handed me a loop of string with a pencil in it and suggested that I loop it around a pair of pegs sticking out of a tabletop, which I did, and attempt to draw a circle that turned out to be an ellipse. At length, she surprised me by pulling out one of the pins from underneath the table and it didn't take long for the pencil to scrawl sporadically and when I stopped, thinking that I had accidentally broken the pin, she urged me to continue - I'll bet you already guessed what figure I was tracing. It didn't take too much intellect to figure what would happen if the string had broken - I'll bet you have already figured that out.

Elsewhere in PF, https://www.physicsforums.com/showthread.php?s=&threadid=6256, There has been a well attended chat during which I found that several denizens of PF including bright Mentor Janus, seemed to agree that the centroid of angular momentum pertaing to the Sun and a planet was not at the center of the Sun but rather at a point between them. Consideration of the overwhelming mass of the Sun it can be assumed that the fulcrum point, when the planet stands at aphelion, remains directionally fixed such that when the planet has traversed half of its orbit (perihelion), the center of the Sun then stands between the planet and the fulcrum. This model would explain an ellipse orbit independent of the alleged Keplerian law that postulates that the Sun is at a focus of the ellipse.
Thanks for your audience, Cheers, Jim

 

[Ambitwistor]

Newtonian gravity does not state that in a Sun-planet system, the Sun's center should be the focus of the planet's ellipse. It states that the center of mass of the Sun-planet sysetm should be the focus of the ellipse. You can verify that for the masses of the planets, the center of mass of any Sun-planet pair lies within the Sun, but not at the center of the Sun. The center-of-mass will always lie between the center of the Sun and the center of the planet.

Of course, when you take into account the fact that the planets interact with each other gravitationally as well as with the Sun, you will find that their orbits are not perfect ellipses, but perturbed slightly from an elliptical shape.

Strictly speaking, the Sun's center would only be at the focus of an elliptical orbit if there were only one planet, and the Sun were infinitely more massive than the planet.

On the other hand, since the Sun is much more massive than any of the planets, planetary motion is very close ellipses with the Sun's center at their focus.

 

[chroot]

Originally posted by NEOclassic
but the notion that the Sun is at a single elliptic focus is ridiculous

Seems to me that a math scholar and a fairly able logician should know that this isn't correct anyway.

- Warren

 

[jimbot]

eliptical axis question

Are the apogees of the planets aligned along a common axis (+-10 degrees)? Or are they scattered around?

 

[Janus]

Originally posted by jimbot
Are the apogees of the planets aligned along a common axis (+-10 degrees)? Or are they scattered around?

Scattered around.
Below is a listing of the longitudes of perhelions of all the Planets in degrees.

Mercury... 77.45645
Venus... 131.53298
Earth...102.94719
Mars...336.04084
Jupiter...14.75385
Saturn...92.43194
Uranus... 170.96424
Neptune...44.97135
Pluto... 224.06676

 

[Nereid]

Originally posted by jimbot
Are the apogees of the planets aligned along a common axis (+-10 degrees)? Or are they scattered around?

Here's a table which can answer your question:
http://ssd.jpl.nasa.gov/elem_planets.html

(In a hurry and can't spare the time to click? Answer to jimbot's first question: No)

 

[Nereid]

To NEOclassic:

If you've got some time (and a few software aids, even XL), you can use the data in the link of my last post to do your own calculations as to where the Sun is, in relation to (any of) the planets, and any elliptical approximations to their orbits. Perhaps you could also share with us a) how you did the calculations, and b) what you found?

 

[NEOclassic]

Originally posted by Nereid
If you've got some time (and a few software aids, even XL), you can use the data in the link of my last post to do your own calculations as to where the Sun is, in relation to (any of) the planets, and any elliptical approximations to their orbits. Perhaps you could also share with us a) how you did the calculations, and b) what you found?

Hi Nereid,
Pardon the delay - I've been finishing an essay on the "mesonic structure of the neutron". I also got around to clarifying my earlier posts in this string. I had said that the sun was not at a focus of planetary ellipses on the grounds that although an ellipse was mathematically perfect there was inconsistency relating to the physical modeling (implied by equal area sweeps rule) that implies that the trajectory velocity at perihelion differs from that at aphelion. Remodeling in such a manner so as to adjust the physical reality to agree with the math, requires the postulation of a virtual massless focus at the position (determined by the eccentricity)between that focus and trajectory a aphelion that equals the distance between the sun-center and the perihelion. When it is considered that the two-body fulcrum, mentioned earlier in this string, cannot cause the planet to have any affect on moving the sun or the virtual focus (that is fixed longitudenally on the major axis) becomes a physical "slingshot".

What happens logically in this model is that, at a given point in the trajectory, the static gravitational attraction between the planet and the sun is determined by the inverse square law using the distance between the planet and the center of the sun; on the other hand, the centrifugal force opposing gravity is the product of the mass*velocity*"distance between the planet and the alternate focus".

I have completed a single sample point (near the aphelion) using this model on the Jupiter orbit with the following conclusion: The gravitational attraction was 2.78*10^45 Newtons and the centrifugal force was 1.88*10^43 Newtons; the ratio of these is 147 but I am not discouraged because the gyroscopic spin of Jupiter that tends to stiffen the trajectory has not yet been reckoned with. It is also possible that the simple placement of the fulcrum that was the inertial moment balance point, might differ in this dynamic model. It is also possible that correction for the fact that the vector in the centrifugal calculation is not necessarily normal to the trajectory

In the near future I hope to repeat the Jupiter point at the mirror position near the perihelion as well review the calculations of all points. In the mean time Cheers, Jim

 

[selfAdjoint]

Neoclassic,

had said that the sun was not at a focus of planetary ellipses on the grounds that although an ellipse was mathematically perfect there was inconsistency relating to the physical modeling (implied by equal area sweeps rule) that implies that the trajectory velocity at perihelion differs from that at aphelion. Remodeling in such a manner so as to adjust the physical reality to agree with the math, requires the postulation of a virtual massless focus at the position (determined by the eccentricity)between that focus and trajectory a aphelion that equals the distance between the sun-center and the perihelion.

This is just not true. The Newtonian two-body solution is perfectly self-consistent and agrees up to a good degree with experiment and measurement. Corrections for GR effects do not do what you say. Of course the speeds at perihelion are different from the speeds at aphelion; that was one of the observed data that had to be explained, and it is visible here on Earth as the fact that "noon by the sun" moves backward through the clock relative to "noon by a uniform clock" during the winter (earth's perihelion is January 2) so that by its max in February it is almost 15 minutes earlier. This is entirely due to the Earth moving faster than average as it approaches and scoots by perihelion. You might also try counting the days from Fall Equinox to Spring Equinox and comparing that count to the number of days from Spring Equinox to Fall Equinox.

 

[Nereid]

Jim/NEOclassic: you may be making things more complicated than they need to be.

Try this: assume there's only the Earth and the Moon (a 2-body problem) and ignore GR for the moment. Assume a circular orbit. Assume the Earth's mass is very, very much greater than the Moon's, perhaps the Moon is just a 'test mass'. Where's the centre of the circle? Where's the Earth?

Now assume the Earth and Moon have equal masses, and are not in elliptical orbits. How do the two bodies orbit each other? in a circle? where's the centre of the circle? what's at the centre?

Now if the Earth:Moon mass ratio is something between 0 and 1, still assuming circular orbits ... where's the centre of the circle(s)?

Finally, if the circles are just very slightly elliptical, more elliptical, ... ?

 

[NEOclassic]

Originally posted by Nereid
Jim/NEOclassic: you may be making things more complicated than they need to be.

Try this: assume there's only the Earth and the Moon (a 2-body problem) and ignore GR for the moment. Assume a circular orbit. Assume the Earth's mass is very, very much greater than the Moon's, perhaps the Moon is just a 'test mass'. Where's the centre of the circle? Where's the Earth?

Now assume the Earth and Moon have equal masses, and are not in elliptical orbits. How do the two bodies orbit each other? in a circle? where's the centre of the circle? what's at the centre?

Now if the Earth:Moon mass ratio is something between 0 and 1, still assuming circular orbits ... where's the centre of the circle(s)?

Finally, if the circles are just very slightly elliptical, more elliptical, ... ?

Hello Nereid,
You have posted five statements that appear to be so ordered that logic alone infers some kind of reality that the truth of your premise is in the final statement. I err! These are not statements but rather questions that imply that the reader has only one of two choices in order to agree or disagree with the ultimate conclusion; if agreement does not happen, then non sequitur's occur and logic is denied. However, I will try to answer your 5 questions (the question hidden in the first statement is revealed if it were to read: "Aren't you making things - - -?"
1. Complication is in the eyes of the beholder - your model is equally complicated to me as my model is to you.
2. It would be clarifying if you were to reveal what effect would exist if GR (I assume you mean General Relativity) had not been ignored. Concentric circular orbits (one for each body) do exist and that singularity is positioned somewhere between the two bodies; when that position is determined by the static balance-beam model an arbitrary position that I call a "fulcrum" can be calculated - there is a caveat that obtains with the static modeling; considering that the system is really dynamic. Assuming that the Earth's mass be very very much greater than that of the moon's obfuscates the reality that most of the solar orbits' fulcrums are at radii from the sun's center less than the radius of the sphere of incandescence contrasted with the earth-moon fulcrum that is away from the Earth's surface as manifest by the Lunar influence on the Earth's oceanic tides. An even more nearly perfect explanation of the position of the true fulcrum is shown by the SOHO space telescopic camera that is adjusted toward that virtual point in an effort to overcome optical aberrations that are evident when eclipses are observed from the face of the earth. The short answer is: [My fulcrum is the center. Viewed from the center of the lunar surface, the Earth is viewed as being constantly at high noon.
3. The quick answer: [For equal body masses, the fulcrum is midway between the diameter of the shared orbit.]
4. I repeat as answered above: [the center of concentric circles is at the fulcrum.]
5. Without a dynamic counter-force to gravitation, a stable orbit would be impossible: If gravity is removed the planet goes off on a tangent and if the planet's motion ceases, it crashes into the sun.

A point I made earlier needs clarification concerning the paradox of the place in a planet's orbital, of minimum velocity. It can be argued that because of conservation of momentum (m*v*r), the smaller "r" is, the larger is the velocity; it follows that the radius is smallest at the position of the minor axis. The paradox becomes evident when the equal-area-sweeps are contrasted at the ends of the major axis - at the perihelion end the apparent orbital velocity is maximum contrasted with a minimum velocity at aphelion. I propose that consideration be given to the notion that the point of reference be moved to the center of the actual ellipse rather than from the focus position. From that reference point the swept areas become congruent as will as equal and total elliptic symmetry obtains. It should be recalled that an invalid assumption that the orbital velocity is maximum at perihelion, suggests that the minor axis has been shifted to the position of the latus-rectum of a parabolic orbit.

I thank you for your audience if you are still here; I have often reminded potential readers who doubt my models to simply treat them as science fiction. To those whose logic, like mine, is constantly tempered by communication with peers, can only find consensus in small degrees because of that human trait: "a mind convinced against its will is of the same opinion still." Cheers.

 

[Janus]

Originally posted by NEOclassic
Assuming that the Earth's mass be very very much greater than that of the moon's obfuscates the reality that most of the solar orbits' fulcrums are at radii from the sun's center less than the radius of the sphere of incandescence contrasted with the earth-moon fulcrum that is away from the Earth's surface as manifest by the Lunar influence on the Earth's oceanic tides. An even more nearly perfect explanation of the position of the true fulcrum is shown by the SOHO space telescopic camera that is adjusted toward that virtual point in an effort to overcome optical aberrations that are evident when eclipses are observed from the face of the earth.

It seems that you are confusing two different points here:

The first is the Barycenter Which is the point around which two orbiting bodies revolve, and the second is the Lagrange point L1, which is a place where the gravitational forces of the two bodies form a point of gravitational attraction.

The first falls under the surface of the Earth while the second is in space between the Earth and moon. (closer to the Moon than the Earth.)

The SOHO probe is placed in a halo orbit around the Earth-Sun L1 point, not the Moon-Earth L1 point. This point is some 1.2 million km sunwards of the Earth. The Earth-sun Barycenter falls within the body of the sun.

I don't know which one your "fulcrum"is supposed to represent, But in either case, they already have terms assigned to them and don't need to be renamed. And of the two, it is the Barycenter about which the bodies revolve.

 

[NEOclassic]

Fulcrum = Barycenter

Originally posted by Janus
It seems that you are confusing two different points here:

The first is the Barycenter Which is the point around which two orbiting bodies revolve, and the second is the Lagrange point L1, which is a place where the gravitational forces of the two bodies form a point of gravitational attraction.

The first falls under the surface of the Earth while the second is in space between the Earth and moon. (closer to the Moon than the Earth.)

The SOHO probe is placed in a halo orbit around the Earth-Sun L1 point, not the Moon-Earth L1 point. This point is some 1.2 million km sunwards of the Earth. The Earth-sun Barycenter falls within the body of the sun.

I don't know which one your "fulcrum"is supposed to represent, But in either case, they already have terms assigned to them and don't need to be renamed. And of the two, it is the Barycenter about which the bodies revolve.

Hi Janus,
My “fulcrum” is merely another name for your ”barycenter”. The only astronomy book in my collection that calls it a “barycenter” was by Karl Kuhn who makes no mention of Lagrangian points, which were uniquely described by Michael Seeds who ignored “barycenter”; Pasachoff (to whom I donated three 2’ x 3’ optical flats for his study of solar energy trapping 30 years ago) failed to mention either of these terms. Jay’s report on the SOHO role in the most recent Solar-eclipse didn’t mention, as I recall, a “halo”. But then again, I’m outside the esoteric group of which you are a member and I appreciate whatever knowledge you pass to me. My current focus is really on trying to adjust the inertial spin-orbit coupling – basic physics makes the point that when the spin and orbit are in the same direction, the dynamically imposed mass enhancement is calculated as follows: I = 2/5 Mass*R^2 (R is the radius of the planet). Without spin the momentum of Jupiter is 1.9 E 27 N; with spin the calculated inertia is 1.35 E 29 N. Considering that the static Newtonian attraction is 2 E 30 N makes believable the possibility that the position of the “barycenter” might differ a little from the statically assumed teeter-totter position. It’s just a suggestion, you know. Thanks for your audience. Cheers,