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Thread: Galactic Orbit and Parallax Measurements

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    Galactic Orbit and Parallax Measurements

    I understand that to measure the distance to nearby stars, we can use a method called parallax where we view a star and then 6 months later look at the star again and by determining how much it moved against the background stars using the diameter of the orbit of the earth around the sun as the base of a triangle to compute the distance. I believe that this would make the base of the triangle about 300 million kilometres. However, at the same time, the sun is orbiting the core of the galaxy at a speed of about 200km/second. By my math over the six months between measurements of the angle to the target star, the sun would carry the earth about 3 billion kilometres around the galactic orbit. Do the astronomers need to take this motion of the earth into account when computing the distance, or are the stars we look at using parallax close enough that we just assume that they are moving at the same speed and have covered the same distance so that this motion cancels out?

    Thank you

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    Quote Originally Posted by lothian View Post
    I understand that to measure the distance to nearby stars, we can use a method called parallax where we view a star and then 6 months later look at the star again and by determining how much it moved against the background stars using the diameter of the orbit of the earth around the sun as the base of a triangle to compute the distance. I believe that this would make the base of the triangle about 300 million kilometres. However, at the same time, the sun is orbiting the core of the galaxy at a speed of about 200km/second. By my math over the six months between measurements of the angle to the target star, the sun would carry the earth about 3 billion kilometres around the galactic orbit. Do the astronomers need to take this motion of the earth into account when computing the distance, or are the stars we look at using parallax close enough that we just assume that they are moving at the same speed and have covered the same distance so that this motion cancels out?

    Thank you
    In most cases the galactic orbital motion of the star we are observing is enough different from the Sun's motion to give it an apparent motion across the sky, commonly called proper motion. The annual parallax oscillation is superimposed on this, causing the star to follow a wavy path across the sky. In a college astrometric exercise I used matrix algebra techniques in a computer program to disentangle the two motions and calculate the values for both components for Barnard's star. Its annual proper motion is about 20 times the amplitude of the parallax oscillation.

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    Quote Originally Posted by Hornblower View Post
    In most cases the galactic orbital motion of the star we are observing is enough different from the Sun's motion to give it an apparent motion across the sky, commonly called proper motion. The annual parallax oscillation is superimposed on this, causing the star to follow a wavy path across the sky. In a college astrometric exercise I used matrix algebra techniques in a computer program to disentangle the two motions and calculate the values for both components for Barnard's star. Its annual proper motion is about 20 times the amplitude of the parallax oscillation.
    Thanks Hornblower, that is very much how I expected, but when you read about parallax, nobody mentions it at all. This would mean that there must have been some very interesting work when they were still working out the galactic orbital speed.

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    The only measurements need to separate the two effects are position measurements over many years, whose precision can be much less than the individual parallax measures because the proper-motion effect is cumulative. There is a technique known as statistical parallax, which uses the drift of the Sun relative to a group of similar stars all around the sky to estimate their mean distance (this mostly dates to the time when individual parallax measurements were much less precise than now).

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    Nobody mention it because a 3 billion km error in a minimum 40 trillion km measurement isnt large.

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    Here's a simulation of Proxima Centauri as viewed from Earth showing both proper motion and parallax.

    http://orbitsimulator.com/gravitySim...iParallax.html

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    I thought that a galaxy is revolving at the same speed wether the star is in the centre or at the extreme edge? Isn't this one of the reasons that dark matter is postulated? If this is so then it doesn't matter where the object star is, as they are all moving the same distance in the same time.

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    Quote Originally Posted by speach View Post
    I thought that a galaxy is revolving at the same speed wether the star is in the centre or at the extreme edge? Isn't this one of the reasons that dark matter is postulated? If this is so then it doesn't matter where the object star is, as they are all moving the same distance in the same time.
    If things were that simple in a real galaxy, parallax measurements would be a lot simpler. If the Sun and all of the stars we observe in astrometric work were in perfectly circular, coplanar orbits around the core of the galaxy, and dark matter made the velocity curve perfectly flat, there would be no proper motion and the parallax effect for the nearby stars would stand out. What we actually have is a significant amount of scatter in the galactic orbital velocities of individual stars, because of differences in their orbital eccentricities and inclinations. These differences are relatively small in proportion to the overall velocities, but are still large in proportion to the amplitudes of the parallax oscillations. For example, Arcturus is in a steeply inclined orbit relative to the galactic plane, and thus from our orbital point of view appears to be moving rapidly on a track nearly perpendicular to that plane. Its annual proper motion is about 20 times its maximum parallax displacement from its mean position.

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    The picture below shows the measurements of the nearby star Vega made by the Hipparcos satellite over a period of about 4 years. You can see that it's pretty easy to separate the curliecues due to the Earth's annual motion around the Sun from the proper motion due to the relative space motion of the Sun and Vega.

    vega_motion_blank.gif

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