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#1 speedster

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Posted 26 January 2022 - 02:50 PM

When I have a future target I'd like to see, given its RA and DEC coordinates, how can I find what day of the year it will cross my meridian at midnight?



#2 CowTipton

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Posted 26 January 2022 - 02:52 PM

https://stellarium-web.org/

 

Search for the object on top

Move the calendar and time on the bottom right.


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#3 speedster

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Posted 26 January 2022 - 05:31 PM

Yes, that may very well be the best way but I'm hoping for an equation using object coordinates and viewing location rather than scrolling through time. 


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#4 raa

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Posted 26 January 2022 - 06:43 PM

Yes, that may very well be the best way but I'm hoping for an equation using object coordinates and viewing location rather than scrolling through time. 

Right.  That's more a navigation thing.  Words like hour angle and co-latitude come into play, I think.  Usually, it's used backward, you take the time when a star culminates and work out your long and lat, taking your local time and gmt difference.  I used to be able to do this, but I've forgot!  So long ago.

 

So let's do it simple like, not exact, but approximate, and Northern Hemisphere (else I'll get confused).

 

0h or Right Ascension CULMINATES (transits the great circle of 0 degrees = 0 h celestial longitude at local midnight) at around the Autumnal Equinox.  So, about 3rd week in September things near 0h RA are getting at their highest at midnight at that time.

 

12h is third week in March, more strictly the Vernal Equinox.  18h RA at the Summer Solstice or around end of the third week in June, 6h, Winter Solstice, end of third week in December.  I've just checked this in a planetarium, going to 0h, 6h, 12h and 18h and checking the transit times for those rough dates at those positions.

 

You've 12 months, you can fill in the gaps.  You don't need the exact value (unless this is a homework thing you've got going on here...) because there's going to be moon, or rain, or somebody's birthday party, or something, you need around a week. either side, even a range of a month will do unless the things is quite Southerly for you.

 

Each month is 4 weeks, so you can get to rough half hours too, as it's 2 hours a month.  You aren't going to observe on the very night at the exact clock strike of midnight.

 

And this should work for local standard time midnight (adjust for the hour of daylight saving otherwise), I think...  I live in UT land, so not sure.

 

Ah, but of course it does!  6h RA transits around midnight on the 20th December 2022 (remember, leap years will affect stuff by a day, hence my just saying "end of third week").

 

There's no need for exact sums.  And as there are twelve zodiacal constellations, and people are often familiar with what constellations lie above and below them, to some extent you can guess what month is best for what constellation, after a while, just from repeat experience.

 

Currently we're near the end of the third week in January, 2 hours a month from above (a 1/3rd of 6 hours, 24 hours, 12 months, so 2h to a month), end of third week in December was 6h for midnight transit, so now it should be around 6+2 = 8h RA.

 

And it is, well just a few days past the end of the  third full week in January, but not quite 8h 30m yet, that'll be around the end of the month, call it 8h 20m.

 

No need for sums and big spreadsheets and looking stuff up, just some cardinal points learnt by rote and then extrapolate at 2h per month past those points.  My targets 8h 20m RA, well, that's more or less tonight then!

 

Well, that's me, might not suit everyone.



#5 astro744

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Posted 26 January 2022 - 09:27 PM

Note the Local Sidereal Time will equal the RA of the target object when it is on the meridian.  You just need to find out when the LST = RA at midnight.  An understanding of celestial navigation would certainly help.

 



#6 Tim Hager

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Posted 30 January 2022 - 11:43 AM

How precise do you need to be?  A quick approximation can be done by knowing that 0 hours RA is on the meridian at midnight on the Autumnal Equinox (approximately September 21st) and 12 hours RA is on the meridian at midnight on the Spring Equinox (March 21st).  For each month later you advance 2 hours.  So for example on November 21st, 4 hours RA will be on the meridian. Make appropriate adjustments for daylight time.   


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#7 havasman

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Posted 30 January 2022 - 02:46 PM

Use the simplest tool available: the planisphere. Easy peasy.

 

Place the object on meridian. Look along the time ring to find midnight. Read the date on the date ring. Done.

 

That method quickly shows Sirius was on meridian at midnight a week after New Years, Procyon was there then a week ago and M44 will be there then next week. Markarian's chain is in that place/time about March 9. M71's there on or about July 29.


Edited by havasman, 30 January 2022 - 03:04 PM.

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#8 Keith Rivich

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Posted 31 January 2022 - 11:41 AM

When I have a future target I'd like to see, given its RA and DEC coordinates, how can I find what day of the year it will cross my meridian at midnight?

Find a copy of Jean Meeus "Astronomical Algorithms". What you seek is in there.



#9 Tony Flanders

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Posted 31 January 2022 - 05:12 PM

Do you want a cookbook formula, or do you want to understand (and possibly derive) how to do this?

 

It should be obvious that the only hard part of this is a formula that for any month M and day D tells you what day of the year the corresponding day is. For instance, February 1 is day 32, and March 1 is day 60 in a normal year and day 61 in a leap year. Various people have given cute algorithms for computing the day of year from M and D, but they're really just ways of encapsulating the number of days per month: 31, 28 (or 29), 31, 30, 31, 30, 31, 31, 30, 31, 30, 31. Which is, of course, quite arbitrary.

 

Then you need to know that the Sun is by definition precisely at Dec 0 at the moment of the vernal equinox, and very nearly at RA 0:00. It moves a full 24 hours of RA in one year, or 365 1/4 days, so knowing what day of the year the vernal equinox falls on, and what day of the year you're interested in, computing the Sun's RA on the relevant day is simple arithmetic (or elementary algebra at worst).

 

True local solar midnight is the moment when the Sun anti-culminates -- i.e. is at its lowest. If an object at RA 0 is at its lowest, then an object at RA 12 is at its highest. So on the vernal equinox an object at RA 12 is highest at true local solar midnight. As luck would have it, true solar time is just a few minutes off from local mean solar time in late March -- in other words, the equation of time is near zero. So if you're on the central meridian for your time zone and not on daylight saving time, objects at RA 12 culminate quite close to clock midnight on the vernal equinox.


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#10 dearchichi

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Posted 01 February 2022 - 09:13 AM

In Stellarium:

- F10, go to the "Transits" tab.

- click on your object of interest

- select days (across 1 year)

- click "Calculate transits"

- check the "Date and Time" column to note when the object transits at midnight

 

Through a script:

- run this Python script (tested on 2.7.18)

- input the object's RA and the observer's timezone and longitude (DEC is not needed)

- the date on which the object cultimnates at midnight is displayed. It accomodates daylight saving time too.

- logic used: figure out the hour angle of the object at midnight today. Find the offset to an hour angle of 24, and determine the number of mean solar days needed to get there, given the 4-minute lead in sidereal time per mean solay day.

- sample output:

 

dateOfMidnightCulmination.png

 

Thanks,

-Shashi

 

 

 


Edited by dearchichi, 01 February 2022 - 09:26 AM.


#11 ButterFly

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Posted 10 February 2022 - 04:11 PM

How precise do you need to be?  A quick approximation can be done by knowing that 0 hours RA is on the meridian at midnight on the Autumnal Equinox (approximately September 21st) and 12 hours RA is on the meridian at midnight on the Spring Equinox (March 21st).  For each month later you advance 2 hours.  So for example on November 21st, 4 hours RA will be on the meridian. Make appropriate adjustments for daylight time.   

With precession, October 1 is a better estimate for J2000.0, and much easier to do in one's head.

 

For example, an RA of 5.5h crosses the meridian at about midnight on ... ?

 

Two hours for every month past Oct 1.  Even hours at the start of the month, odd hours in the middle.  Half hours are about a week.

 

5.5 is about 6, so 6/2 is three months after Oct 1.  6h would be about Jan 1.  But it's 5.5h, so subtract one week.

 

Also works the other way.  Today is Feb 10, about a week after Feb 1.  Feb 1 is four months away from Oct 1, so an RA of about 8h crosses meridian on midnight.  Feb 10 is between about a week and two weeks later, so about 8.5-9h crosses meridian around midnight tonight.

 

Adjust for daylight savings time afterward.




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