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We take observations from earth but to define radial velocity, transverse velocity and the proper motion of stars, why we consider them with respect to the sun? and then we do some corrections due to both rotational and orbital motion of the earth.

Why can't we directly consider these motions with respect to earth instead of Sun?

And what is the whole procedure of correction?

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The Earth is a moving (actually, accelerating) platform from which we make our observations. If you want to describe the motion of a distant celestial body, then it does not make much sense to provide a geocentric velocity, because this will depend on exactly when the observations were taken (because the Earth orbits with a speed of about 30 km/s, but the velocity changes throughout the year), the position on the Earth that the measurement was taken (because the Earth's equator revolves at around 0.5 km/s, but this is different at different latitudes) and the position of the star in the sky (because the previous two effects have to be resolved in the direction of the star).

Given that, then it is far easier to quote a velocity in a frame of reference that does not depend on these things. One can use the heliocentric frame in most circumstances - that is the frame of reference in which the Sun is stationary. To do this, one has to remove the components of the Earth's orbital and rotational velocity. However, if very precise measurements are being done then it is better to use the barycentric reference frame, which is with respect to the centre of mass of the solar system (since the Sun orbits this with a speed of around 0.1 m/s).

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  • $\begingroup$ But the sun is also moving and accelerating? $\endgroup$ – Cubic Jul 2 '18 at 12:32
  • $\begingroup$ @Cubic Indeed and so are other stars that we might measure, but the relevant timescales for changes in velocity are much longer than a year (bar the motion around the solar system barycentre, which I mention). $\endgroup$ – Rob Jeffries Jul 2 '18 at 13:45
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We use the position of the sun (or more accurately the centre of mass of the solar system) as this gives us a very nearly inertial frame of reference. An inertial frame is one which is not changing its velocity. The surface of the Earth does not define an inertial frame.

The Earth orbits the sun and so it is moving in opposite directions in summer and winter. If we were to use the radial velocity (for example) relative to the Earth, we would get a different value in summer from winter. The orbital speed of the Earth is about 30km/s, and the radial velocity of stars tends to be in the 10s of kilometers per second, so the Earth's motion is a significant amount. If, however, we use the centre of mass of the solar system (which is always very close to the sun) then we can record the actual motion of the star.

The process of finding the relative motion is to measure the radial motion relative to the telescope doing the observations, and then subtract the velocity of the Earth around the sun, and the velocity of the telescope relative to the centre of the Earth. Since these two velocities are well known, compensating for them is essentially no more than subtraction.

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  • $\begingroup$ Summer/winter should rather read aphelion and perihelion. $\endgroup$ – rexkogitans Jul 2 '18 at 5:43

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