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As it is explain here, we can determine the speed a luminous body along the direction of the line of sight in the sky; moreover, with enough long observation, we can observe how much the body change its position in the sky, but how can we actually determine how far is this body from Earth, and what is it's velocity ?

I mean without knowing how far the body is, we cannot say anything about its speed along perpendicular to the line of sight from its proper motion in the sky.

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If we known the intrinsic luminosity of the star, then we can determine its luminosity distance from the fact that the apparent luminosity of the object will diminish with the square of the distance. The intrinsic luminosity can sometimes be inferred from other observable qualities such as the temperature or variability (depending on the type of object).

For stars that are not too distant we can also use stellar parallax to measure their distance. As the Earth (and we with it) move around the Sun, the position of nearby stars shifts compared to distant stars (see diagrams on Wikipedia page). The size of this shift is (approximately) inversely proportional to the distance. This type of measurement is the fundamental basis for most distance measurements in astronomy. In fact the most common distance unit in astronomy, the parsec, was originally defined as the distance of an object with a parallax of 1 arcsecond.

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  • $\begingroup$ Thank you for your answer @mmeant, but how can people were able to measure the temperature of a star in the beginning of 20th century ? I mean now, I guess, we can use infrared telescope for that, but what about then ? $\endgroup$
    – Our
    Apr 7, 2018 at 3:18
  • $\begingroup$ Moreover, the method of stellar parallax assumes that the luminous body is at rest wrt to Sun, which is not the case in general, so isn't this going to cause problems ? $\endgroup$
    – Our
    Apr 7, 2018 at 3:22
  • $\begingroup$ @onurcanbektas. To determine the temperature of a star you take its spectrum (and fit a black body curve). The technology to do this was certainly around at the start of the 20th century. (Hell to first approximation you can do this by eye: blue stars are hotter than red stars.) $\endgroup$
    – TimRias
    Apr 8, 2018 at 18:55
  • $\begingroup$ @onurcanbektas. Peculiar motion does not form a significant problem for parallax measurements. The stellar parallax is going to be periodic with a period of a year. You can easily separate this from a secular peculiar motion of the object. $\endgroup$
    – TimRias
    Apr 8, 2018 at 18:57
  • $\begingroup$ How exactly can we do that ? Is there any chance that you can provide me a reference for that ? $\endgroup$
    – Our
    Apr 9, 2018 at 3:01

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