Conversion of units (tangential velocity)

[rbnphlp]

This should be very easy but I can't see what I am doing wrong...

$$V_t=\mu .d$$ where vt = tangential speed (in km/s)
d = distance (in km)
mu(radian/sec)

Now by converting I should get

$$V_t=4.74\mu .d$$
vt = tangential speed (in km/s)
d = distance (in parsec)
mu(arcsec/yr)

but according to my working ,
$$V_t=\frac{206264\times 365 \times 24 \times 3600}{3.086 \times 10^{13}}$$

which comes to be $$V_t=.21\mu .d$$

I know inverting the above fractions will lead me to the answer but I can't see why ?:(

1parsec=3.086*10^13 km
1 radian=206264 arcsec

Thanks ..

 

[mathman]

It would help if you described the original problem.

 

[Integral]

If you were to attach your conversion units to the numbers you have, (ie 365 day/yr) then do all of the algebra in units I think you will find your problem.

Note that after completing the conversion the units of the resulting velocity will NOT be in km/s.