Thanks for your reply. I did a small test with relative measurement and though the object moved in circular orbit, the time compression and expansion (that is how it is visualized) while measuring caused it appear as if it is moving in elliptical orbit.

I will need a picture to show you how the time compression / expansion takes place that gets translated in to elliptical orbit when the object itself moves in circular orbit.

I will send you my mathematical analysis in neatly prepared document. In the mean time, I would like to know how the earths orbit is traced to conclude that it goes in elliptical orbit? If you have a document or some one who measured it, would give me detail on what is the procedure with which it was measured that would be great.

I can very easily challenge the inference.

Here is my argument on this:

Take a disk with central hole 1 inch radius call it as A, Then at 3 " radius make another hole (small hole call it as B and at 6" make another hole C

Connect by string (measurement limb) that is a-b and b-c.

When you rotate the disk, then A is center(represents Sun). B moves relative to A (center) and C moves Relative to center A which is a relative object with which the measurements were taken.

All make a rotation with respect to center at 2-Pi radians angular velocity.

When you measure relative to each other then when C is at 90 degrees vertical and B is at 45 degrees to vertical, C, B, A all moves at same speed. When the reference point is Horizontal axis (A) then for every movement of 10 degrees C, B also makes 10 degrees,

But sinusoidal nature of the movement translates it to small distance in coordinate plane. The rate of vertical and horizontal movements in co-ordinate plane is going to be smaller for B.

In a single mathematical formula will be

(R sin (Theta + Delta ) - r sin(theta)) / 2   will give location of B where R is the outer most orbit and r is the outer edge of inner object A which is a reference point of A (Sun).

This in coordinate plane appear as if the movement is non linear though the angular velocity is linear. This conversion makes it to appear as though the object B's velocity is not uniform. If you consider the velocity is uniform, then it should be treated as there was a time compression / expansion that had taken place. Since the time doesn't compress or expand, and velocity of object had not changed, the only alternate is to cover more distance during part of the cycle. That is how the elliptical orbit was determined.

In practice, the object moved in perfect circular orbit relative to center despite the fact that the time got compressed and expanded that can be visualized as if it had moved in elliptical orbit with respect to a linear time scale.

The explanation will be good if you have a drawing and detailed plot of the graph.

This time compression and expansion due to translation from angular motion to coordinate plane of measurement would easily fake you to believe that the body moved in elliptical orbit instead of circular orbit.

My point is that Kepler wasn't aware of this correction that needs to be applied.

Since the measurements are always made relative to each other, as long as you make relative measurement, this correction need to be applied to both reference and relative object as it may cancels out, hence you may have seen the impact in practical application while doing adventures in space.

But inappropriate evaluation will lead to mathematical anomaly or measurement error or wrong result.

Hence I strongly feel that Earth moves in circular orbit but relative measurement causes it to appear as if it moves in elliptical orbit.

This measurement error can be physically seen if you measure the earths orbit starting on Jan 1 2007 and measure all the way till Dec 31 2007 which will trace an ellipse which is different from measurement started on say May 1 2008 all the way through April 30 2009.

These two will trace two ellipses which won't fit the same path. This will prove whether the earth is moving in circular or elliptical orbit.

I am not sure who will take up this job and get precise result.

Let me know your thought on this?

On the other hand I would like to know how it is being traced and who measured and what is their result? Any knowledge transfer will be greatly appreciated that would help me fix my theory if I am wrong.

 Post your replies, I will give it a deep thought and publish a document.

Hi Guys It is a challenge to existing theory, I own it !! Just kidding.

The kind of time compression you're envisioning certainly occurs at relativistic velocities. The Earth is hardly moving at relativistic velocity!

To posit that sub-relativistic time compression or dilation occurs, you'd first have to suggest and demonstrate the mechanism or reason for it happening. Sooner or later that would have to be demonstrated and verified. This has happened for the difference between high-orbit spacecraft (the GPS satellites, for example) versus ground-based clocks, but the difference is so slight as to become important only over many orbits.

You're also ignoring the effects of other bodies in the solar system, most notably Jupiter. There are so many other bodies involved that the chances for a circular orbit are, as I said before, practically nil.

I follow your reasoning about Kepler, but -- again -- the velocity difference must be a significant fraction of the speed of light.

There is also a component of this involving the Sun's mass warping spacetime (which is why we orbit in the first place) and it is now known to be affected by what is called frame dragging. But that wouldn't account for the 2% difference.

You're assuming a circular orbit and figuring what must change to keep it that way (time) -- to make it fit the observed variance. It is something like this, which describes the way shuttle and satellite orbits are computed.

Kepler approached this the other way around -- he changed the orbit's shape to fit the observed variance. In one sense, they're two sides of the same coin.

However, if the orbit were circular, then affects such as those noted here would be different.

Climatologists are keenly interested in the Earth's orbital parameters. Citations and a calculator are here.

A good graphical, geometric, and trigonometric description of the orbital parameters is here.

We have had a similar discussion here in the past (another member name). If I remember correctly, that deteriorated into a belief versus science discussion (where Geocentrism reared its head). If this becomes a matter of faith versus science, then it needs to be taken to the Off-topic Discussions forum.

Welcome to the discussion group, Viswamitra.

Kepler knew the distance between Earth and Sun (in astronomical units, not miles) at any time of the year by the apparent angular diameter of the Sun.  This is how he knew the orbit was eccentric, but not necessarily elliptical. To prove the latter, he had to study Mars as described below.  I'll first mention that Kepler noted the positions of Mars in the sky separated my one Martian year.  He also knew the positions of the Earth relative to the Sun, and using trigonometry he determined the position of Mars in three-dimensional space.  By applying this procedure at many points along Mars orbit, he proved that Mars' orbit was not only eccentric, but also elliptical. 

We are actually discussing the reference (unperturbed) ellipse traced around the Sun by the barycenter of the Earth-Moon system during a specific epoch.  At 2000.0 the eccentricity (off-centeredness) of that ellipse was 0.01670863, i.e the aphelion distance was 1.01670863 times the length of the semi-major axis.  Indeed, the orbit is virtually circular since that corresponds to an ellipticity (non-circularity) of only 1.00013962, i.e. the major axis is 1.00013962 times the length of the minor axis.  A person looking at a diagram of this orbit could not tell it from a circle, but it might be somewhat obvious that the Sun is not exactly at the center. 

Far too often authors refer to a certain effect being due to a planet's elliptical orbit when they really mean the off-centeredness of the Sun.  The two concepts are related, but they are not the same thing.  However, in the cases of many comets the ellipticity becomes quite noticeable.

Kepler knew that the Sun was not exactly in the center of a planet's orbit. However, his initial assumption was that each orbit was circular.  Indeed, it was reasonable to think that an orbit could be both eccentric (Sun not exactly at center) and circular.  It was because Kepler used quite precise naked-eye data from Tycho and chose Mars (relatively high ellipticity) as his research case, he was able to determine that Mars' orbit was slightly elliptical.  If he had waited a few more years for telescopic data, he would have been confounded by planetary perturbations that distorted his ellipses. 

Thanks a lot for giving me some references. More over your points makes sense to me. I will go over the document and give it  deep thought. As I said It is not my aim to find flaw with established law and verified result.

You guys are wonderful and expert with indepth knowledge.

Thanks

The analemma demonstrates that the Earth's orbit is elliptical.

http://en.wikipedia.org/wiki/Analemma

http://www.analemma.com/Pages/framesPage.html

http://www.perseus.gr/Astro-Solar-Analemma.htm

Dave Mitsky

DaveMitsky wrote:

The analemma demonstrates that the Earth's orbit is elliptical. ... Dave Mitsky

Of course! (slaps head) ... and the equation of time (horizontal component) speaks directly to the point made ... brilliant!

DaveMitsky wrote:

The analemma demonstrates that the Earth's orbit is ellipitical.

The asymmetry of both the analemma and equation of time demonstrate that there is a variance of the angular velocity of the Earth as it moves around the Sun.  This provides a clue that the orbit might be eccentric, but does little to indicate it is elliptical.  As I discussed earlier in this thread, there is a common misconception regarding the terms eccentricity and ellipticity.  They are not the same thing, although in the realm of celestial mechanics there is a mathematical relationship between them.  But until this was proven by Kepler, there was no reason to doubt his initial assumption that the planets' orbits were both circular and eccentric, i.e. circular, but with the Sun not at the exact center. 

While the 2000.0 mean eccentricity of the Earth's orbit was 0.01671, its ellipticity was 1.00014.  The latter figure means that the major axis was 0.014% greater than the minor axis.  This miniscule variance from a circle could not be deduced by eyeballing an analemma or a diagram of the orbit.  However, the fact that the Sun would be shifted from the center of the orbit by 1.7% of the length of the semi-major axis should be apparent to someone carefully studying that orbital diagram.  But in understanding the meaning of the more extreme deformation of the analemma, one must have knowledge of Kepler's Second Law regarding how a particular planet's varying distance from the Sun affects its angular velocity.