Orbital speed of Earth

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by makis</i>
<br />Has the orbital speed of the Earth been measured experimentally and if so, do the results agree with the theoretical numbers obtained from the solution of the kinematic equations of its elliptical motion around the sun?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Yes and yes. For example, we measure high-precision doppler shifts in quasars and pulsars that would not be constant if our calculations of Earth's orbital speed were not right on target.

At a more basic level, speed is a distance traversed in a time interval. So measuring location and time eventually turns into measures of speed, and these (naturally) are consistent with doppler shifts. We now get 8-9 digits of precision in such measures with modern high-precision techniques such as VLBI or radar and laser ranging or spacecraft transponders. -|Tom|-

If there are very accurate measurments of the orbital speed can the data be accessed? How much is the speed effected by the moon?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />If there are very accurate measurments of the orbital speed can the data be accessed?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Same answer as many times before: See the National Space Sciences Data Center (NSSDC). Modern high-precision data is not trivial to use. But it is all available to everyone, and the knowledge about how to use it is taught in graduate schools.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">How much is the speed effected by the moon?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">+/- 12 meters/second. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by makis</i>
<br />Has the orbital speed of the Earth been measured experimentally and if so, do the results agree with the theoretical numbers obtained from the solution of the kinematic equations of its elliptical motion around the sun?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Yes and yes. For example, we measure high-precision doppler shifts in quasars and pulsars that would not be constant if our calculations of Earth's orbital speed were not right on target.

At a more basic level, speed is a distance traversed in a time interval. So measuring location and time eventually turns into measures of speed, and these (naturally) are consistent with doppler shifts. We now get 8-9 digits of precision in such measures with modern high-precision techniques such as VLBI or radar and laser ranging or spacecraft transponders. -|Tom|-
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

If I understand correctly how ranging instrumentation works, the only possible measurement is the relative radial speed between two or more bodies in motion.

For a planar orbit in polar coordinates, the velocity v is given by:

v = (dr/dt)ru + r(d8/dt)8u, where the number 8 used used for the angle theta and ru and 8u are the untit vectors.

Thus, knowledge of the instanteneous radial speed dr/dt does not suffice to determine the magnitude of v ( v dot v). Knowledge of the instanteneous angular speed d8/dt is also required.

How is the instantenuous angural speed is determined to plot |v| as a function of t? If an elliptical orbit is assumed in the first place then it is only natural that experimental and theoretical data will match to a high degree.

In the case of the sun-earth system how to you use ranging equipment for an empirical determination of the orbital speed changes?

I doubt there is any pure empirical evidence based on measurements that confirms the elliptical orbit of the earth around the sun and I suspect the available data is a 'model', that is extrapolations via the use of ad-hoc hypothesis about the shape of the orbits in the planetary system.

By the way I think that JIM is right to protest this for some time now. There is plenty of data available but nothing to prove the data can replicate the theory sssolely on empirical grounds.

Makis

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by makis</i>
<br />If I understand correctly how ranging instrumentation works, the only possible measurement is the relative radial speed between two or more bodies in motion.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Sorry, but your understanding is not correct. Ranging measures the round-trip time of flight for a radar or laser signal between the source and target bodies. Time of flight multiplied by speed c gives distance between source and target bodies, with a typical precision of 8-9 figures. So ranging measures distances, not velocities. The time rate of change of ranges gives velocities.

It goes without saying that one must then allow for where the transmitting station was relative to the center of the Earth at transmission, where the reflection point was relative to the target body's center, and where the receiver was at reception. Such ranges give the best measurements we have for planet positions relative to the Sun and to each other. But ranging can't do it all because they do not indicate orientation. So this data is combined with optical observations of positions relative to the star background, so that we have all three coordinates for the position of each body relative to each other body.

The nature of your questions suggests some confusion about how we can be so sure it is not all a house of cards. Perhaps the best of several checks is provided by pulsars, which are effectively radio beacons transmitting rapid pulses on a known schedule. They are as good as atomic clocks, perhaps better in some ways. So if you were blind and could see nothing else, you could still tell exactly where you were in all three coordinates by observing these "time signals" arriving from pulsars in many different directions around you. Because the signals travel at the speed of light, if you receive "pulse A" from "pulsar X" early, you must be closer to that pulsar than you thought by an amount you can calculate. And likewise for measures from all the other pulsars.

So you see there is no room for ambiguity. Between pulsars, ranges, and optical data, we know our precise position and velocity relative to the Sun and the other solar system bodies.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If an elliptical orbit is assumed in the first place then it is only natural that experimental and theoretical data will match to a high degree.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Few people today have any use for assumptions about "ellipses" because, at this level of accuracy, no orbit is an ellipse. We deal with the actual, 3-dimensional motion. Ellipses are still used by astrologers for horoscopes, but are too crude for modern high-precision work. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by makis</i>
<br />If I understand correctly how ranging instrumentation works, the only possible measurement is the relative radial speed between two or more bodies in motion.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Sorry, but your understanding is not correct. Ranging measures the round-trip time of flight for a radar or laser signal between the source and target bodies. Time of flight multiplied by speed c gives distance between source and target bodies, with a typical precision of 8-9 figures. So ranging measures distances, not velocities. The time rate of change of ranges gives velocities.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I basically said the same. Differentiation of position data gives velocities. I have done enough experimental work with interferometers to know that.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
It goes without saying that one must then allow for where the transmitting station was relative to the center of the Earth at transmission, where the reflection point was relative to the target body's center, and where the receiver was at reception. Such ranges give the best measurements we have for planet positions relative to the Sun and to each other. But ranging can't do it all because they do not indicate orientation. So this data is combined with optical observations of positions relative to the star background, so that we have all three coordinates for the position of each body relative to each other body.

The nature of your questions suggests some confusion about how we can be so sure it is not all a house of cards. Perhaps the best of several checks is provided by pulsars, which are effectively radio beacons transmitting rapid pulses on a known schedule. They are as good as atomic clocks, perhaps better in some ways. So if you were blind and could see nothing else, you could still tell exactly where you were in all three coordinates by observing these "time signals" arriving from pulsars in many different directions around you. Because the signals travel at the speed of light, if you receive "pulse A" from "pulsar X" early, you must be closer to that pulsar than you thought by an amount you can calculate. And likewise for measures from all the other pulsars.

So you see there is no room for ambiguity. Between pulsars, ranges, and optical data, we know our precise position and velocity relative to the Sun and the other solar system bodies.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Is this a wish or something that referes to actual, undisputable data? IMO based solely on measurements and observations, this is not possible. Do you know where I can get that Earth velocity graph relative to the Sun that is based solely on observations?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If an elliptical orbit is assumed in the first place then it is only natural that experimental and theoretical data will match to a high degree. Few people today have any use for assumptions about "ellipses" because, at this level of accuracy, no orbit is an ellipse. We deal with the actual, 3-dimensional motion. Ellipses are still used by astrologers for horoscopes, but are too crude for modern high-precision work. -|Tom|-
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I thought astrologers use the geocentric system, something very similar if not identical to the Ptolemaic system, where the motions of planets are epicycles resulting in retrogate motion.

So what is the 'actual', 3-dimensional motion of the Earth around the Sun? If it's not an ellipse, what does it look like? Any references or links to graphs?

Makis