Proper Motions​

 

According to SIMBAD, the proper motion in right ascension direction (east/west) for Alkaid is -121.17 mas/yr. Its proper motion in declination direction (north/south) is -14.91 mas/yr. And, its radial velocity is -10.9 km/sec.

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To find the tangential velocity for Alkaid, we must first use the formula μ = √Ra ² + Dec ², where μ = proper motion, Ra = right ascension and Dec = declination.

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μ =
Ra = -121.17 mas/yr
Dec = -14.91 mas/yr

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μ = √Ra ² + Dec ²
μ = √121.17 mas/yr² + -14.91 mas/yr² = 121.92 mas/yr

 

Next, we must convert mas/yr into km/sec. To convert we divide by 1000.

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(121.92 mas/yr)/1000 = .12192 km/sec

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Then, we use the formula Vt = μ(4.74d), where distance = 31.87 parsec (found in the angles in parallax lab above.

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Vt =
μ = .12192 km/sec
d =31.87 parsec

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Vt = μ(4.74d)
Vt = 2192 km/sec (4.74 x 31.87 parsec) = 18.44 km/sec

Now, we can use our tangential velocity of 18.44 km/sec to find the space velocity for Alkaid. To do this we use the formula Vs = √Vr² + Vt².

 

Vs =
Vr (from SIMBAD) = -10.9 km/sec
Vt = 18.44 km/sec

 

Vs = √Vr² + Vt².
Vs = √-10.9 km/sec ² + 18.44 km/sec ² = 21.42 km/sec

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