Copernicus & GR

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Copernicus & GR
« on: 22/06/2012 10:01:09 »
In the 20th century, orbits are explained by general relativity, which can be formulated using any desired coordinate system, and it is no longer necessary to consider the Sun the center of anything." wikipedia/ Copernicus page.   I dont get it, please clarify, thanx


Offline CliffordK

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Re: Copernicus & GR
« Reply #1 on: 22/06/2012 11:34:16 »
You could think of the Earth as hurtling through space at about 370 km/s with respect to CMBR, with its direction and velocity constantly being altered by the gravitational pull of the sun, the moon, the 8.5 planets, and the 300 billion stars in the Milky Way.

But, this isn't anything new.  Neptune was discovered in the 1800's by carefully observing anomalies in the orbit of Uranus.


Offline evan_au

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Re: Copernicus & GR
« Reply #2 on: 22/06/2012 13:47:19 »
A "coordinate system" is how you measure the position of things, and how far apart they are.

  • Before Galileo, philosophers and astronomers thought of the earth as the center of the universe, so you would measure distance from the Earth. And this is probably close enough if you are mainly interested in the orbit of the moon, and when there might be an eclipse.
  • Copernicus suggested that the orbits of planets might be easier to calculate if you measured their distance from the sun.
  • This was certainly true for Kepler and Newton in their analysis of the elliptical orbits of the planets, where the sun sits at one of the foci of the ellipse. This is fine if you are mainly interested in the orbits of the planets.
  • It was with the mapping of the galaxy in the 1900s that astronomers identified motions within our galaxy.
  • With Hubble's work, the motion between galaxies was measured.
  • Later, the Cosmic Microwave Background Radiation (CMBR) was discovered, and you can measure relative to the CMBR.
Each of these psychologically removed the earth one step further from the center of the universe.

So, what's the best coordinate system (or "frame of reference") to make your measurements?
It mainly depends on what problem are you trying to solve!
  • Throwing a ball: It's good enough to consider the playing field as the coordinate system. The maths is very easy.  (The Sun, Moon and planets won't affect the result measurably.)
  • Launching a satellite into low earth orbit: It's convenient to consider the center of the earth as your frame of reference.
  • Sending a mission to Mars: You have to consider the Sun and planets, so the Sun is probably the simplest frame of reference
  • Voyager studying the Heliosphere: It is probably easiest to use the center of our galaxy as the frame of reference (the planets and other galaxies are too far away to impact the results much).
  • The LHC studying collisions of protons at near light-speed: You can still take the earth as your "stationary" frame of reference, but some behaviors like particle half lives have to take into account that the particles have their own frame of reference.

The theory of relativity explicitly states that the choice is fairly arbitrary.