How do I apply specific astronomy concepts I have learned to calculations?

Question

Hi, I have a few questions about concepts I've learned and using them with equations.

Firstly, I know there are differences in calculations when it comes to north and southern hemispheres. When calculating the maximum altitude of a star, if the star has a positive declination, but is observed from the southern hemisphere, does the equation become h= dec + 90 degrees - (-latitude) to account for the southern hemisphere?

Secondly, when calculating tangential velocity, I understand that it is the proper motion (arcsecs per year) multiplied by the distance to the star (in parsecs) (so vt= proper motion * d), but then what are the units of the resulting answer? Would the tangential velocity be in parsecs/year? How do I get it to be in m/s?

Finally, how do I convert Julian date to UT time? If for example, the given Julian date is 2455955 I use the equation J=2000 + (JD-2451545)/365.25, I get the answer 2012.07. But what does this mean? How do I get this to UT time?

Thank you

Answer 1

In Northern hemisphere

h = 90 + (dec - latitude)

In Southern hemisphere

h = 90 - (dec - latitude)

In Southern hemisphere both the star's declination and

your latitude are measured with opposite sign.

If angular velocity is in arcsec/year, and distance is in parsecs,

then velocity is in arcsec×parsec/year.

In order to convert it to m/s you do it like any other conversion:

arcsec = 2π/(360×360)

parsec ≈ 3×10¹⁶ m

year ≈ π×10⁷ s

Therefore

arcsec×parsec/year ≈ (2π/(360×360))× 3×10¹⁶ m / π×10⁷ s ≈ 50000 m/s

2012.07 means 0.07 of a year past noon of January 1, 2012.

0.07 of a year is about 25 days, which would give you January 26, 2012.

You can also calculate the exact hour and second, but you need to keep in mind two things:

1) Make the calculations more precise.

(The number 2012.07 is rounded, making calculation of time meaningless.)

2) Julian time starts at noon, while UT time starts at midnight.