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Suppose a star in the ecliptic plane has a parallax of p = 0.5 arcsec and a proper motion perpendicular to the ecliptic plane of µ = 1.0 arcsec/year.

I need to describe the path that the star appears to move around on the sky, with respect to distant background objects, over the course of several years.

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i am taking some assumptions here : that the preccession of earth does not change the ecliptic w.r.to earth's equator. then:

the perpendicular movement MUST be due to the relative velocity of the star w.r.to sun.

the position of star w.r.to distant stars as seen form earth ( for a particular time on a sidereal day, plotted day after day , all at a particular place ) will be like this :

component parallel to ecliptic moves sinusoidal with time ( with an amplitude of .5 arcsec and time period of 1 year ) component perpendicular will move linear with time ( speed : 1 arcsec/year ) overall, it moves like a sine wave. enter image description here
( y axis : line of ecliptic )

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  • $\begingroup$ Thanks for the help. What would change if we had the same values but this time the star is at coordinates l=96.4 and b=29.8? The coordinates of the North Ecliptic Pole. $\endgroup$
    – cf12418
    Commented Feb 15, 2015 at 17:01
  • $\begingroup$ star wont be on the ecliptic, and is on north celestial pole. the ecliptic is 23 degrees inlcined with celetial equator. as the star is moving overall in an year, we see it's speed parallel component ( sin(23deg) arcsec/year ) and moves perpendicular to thta motion sinusoidally with time (parallax) . so it is same as the picture , with change in speed as sin(23deg) instead of 1 arcsec/yr . $\endgroup$
    – NIkhil Reddy Ramolla
    Commented Feb 16, 2015 at 2:08

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