STARS MOTION AND HOW IS IT SEEN FROM EARTH? By: Paul Jones & Antoine Henderson PROPER MOTION & TRANSVERSE VELOCITY • Proper motion is equal to angular displacement (in arc seconds) divided by time. Ex: 300’’/50 yrs PM= 6 years of that star. • Transverse velocity is equal to the distance divided by the constant 3.2 x 10 7 th seconds. Ex: TV= 4000000000km/ 3.2 x 10 7 th seconds therefore TV= 125 km/s RADIAL VELOCITY & TRUE SPACE MOTION • Radial Velocity is equal to (apparent wavelength / true wavelength -1) (c). • Ex: RV=(399.85 / 400 -1) (300,000) RV = (-.000375) (300,000) RV= -112.5 km/s or 112.5 km/s • True Space Motion = sq. root of radial velocity sqrd. + transverse velocity sqrd. • Ex: TSM= sq root of (112.5 km/s)sqrd. + (125 km/s)sqrd. TSM= sq root(28281.25) TSM= 168.17 km/s STELLAR PARALLAX • Astronomers use stellar parallax with stars through a series of steps such as follows. 1. First they look at the star from one part of Earth’s orbit make measurements and then perform the same process on the other side of the orbit. 2. This is due to the great baseline needed to measure even the closest stars. 3. After having found the parallax and knowing the baseline to be 2 A.U. astronomers can then determine the distance to the star. • This process however can only be used on a few of the closest stars due to the large distances that make the parallax extremely small. • In fact they are so small that degrees aren't used, instead they use arc seconds which when translated one arc second is one parsec and through determinations 1 parsec is 206,265 A.U.’s or 3.3 LY. That gives you an idea of how small the angles really are. USING AN INVERSE SQUARE LAW WITH LUMINOSITY AND APPARENT BRIGHTNESS • The inverse square law shown below represents the factor of squaring the are a certain portion of light from a star has to fill. (2 times farther is 2 squared thereby making the area the same amount of light having to cover 4, if it is 3 times farther it has to cover 9 times the area, so on and so forth). So by using this formula we can determine distance based on luminosity and apparent brightness or energy flux. This also helps with understanding of how bright a star really is. Ex: If two stars have the same apparent brightness yet one star through calculations is substantially farther away therefore the farther star must either be much hotter and brighter/bigger or both. HOW DOES THIS SHOW MOVEMENT • By using these calculations and using them over time we can see small changes in how stars move. Similarly when we watch a star spin we see red and blue shifts as it spins away and at us while rotating. But by constantly watching and using Proper motion and transverse velocity we can see movement with help from the previous ways of calculating distance. By using these we can also determine if a parallax shifts as well as if the distance changes thereby determining whether a star is moving or not.