What we know: Right ascension (RA) and declination (Dec) are a coordinate system for celestial objects that correspond with longitude and latitude respectively. Because the problem only concerns the location of AY Sixteenus relative to our Meridian, we can ignore declination for the sake of this problem. Consequently, let's look closer at RA:
Image from: http://en.wikipedia.org/wiki/Right_ascension
Right ascension is measured eastward from the vernal equinox, which we know from question 2, has the unique property of being 00:00 LST at noon on March 20th.
Solve: With the background information we know, the first part of the problem seems much easier, almost a trick. If the RA of the star is 18, its LST will always be 18:00 hours, regardless of the day of the year. So the star will be at 18:00 LST on the first of every month. The thing that does change, however is at what time the star is on our meridian.
So now we can tackle the last part of the problem. We need to find when the star would be on our meridian at midnight solar time (this is my interpretation, confirmed by John during TALC). To visualize this we can draw another diagram.
Update: After another visit to TALC and another talk with John, I realized where I went wrong. I understood that LST was measured from Greenwich, like UTC, but that is incorrect because it is local standard time, measured from your location. Then we only have to correct for 6 hours, and at a rate of 2 hours a month, the star would be on our meridian 3 months after the vernal equinox. This would be around June 20th, not August 20th like I originally found.
Solve: With the background information we know, the first part of the problem seems much easier, almost a trick. If the RA of the star is 18, its LST will always be 18:00 hours, regardless of the day of the year. So the star will be at 18:00 LST on the first of every month. The thing that does change, however is at what time the star is on our meridian.
So now we can tackle the last part of the problem. We need to find when the star would be on our meridian at midnight solar time (this is my interpretation, confirmed by John during TALC). To visualize this we can draw another diagram.
Because the star is 18 hours away from 0, if we convert that to degrees: \[18\: hours \cdot \frac{15\,^{\circ}}{1\:hour} = 270\,^{\circ}\] so that means that at 0:00 LST, the star is on the meridian of \(90\,^{\circ}\) W. Our longitude is only \(19\,^{\circ}\) away (because the Earth spins East) so the star will be on our meridian \[19,^{\circ} \cdot \frac{1\:hour}{15\,^{\circ}} \approx 1 \: hour \: 6\: min\] one hour and six minutes later at 19:06 LST, or 18 hr + 1 hr & 6 min from noon on March 20th. 19:06 sidereal hours from noon would be 7:09 UT (accepting a difference of 4 min a day).
Finally, all we need is to find is when the star would be on the meridian at midnight, local time. 7:09 UT would be 2:09 EST due to the five hour time difference. 2:09 in the morning is 9 hours 51 minutes from midnight or 591 minutes away from midnight (9 x 60 = 540 min + 51 min = 591 min). From problem 2, we can do the same 4 min/day conversion to find:\[591 \:min \cdot \frac{1 \: day}{4\:min} \approx 148\: days\] 148 days after March 21 would be August 16th!
Acknowledgements: Thanks to John for his help at TALC to get started on this problem.
Update: After another visit to TALC and another talk with John, I realized where I went wrong. I understood that LST was measured from Greenwich, like UTC, but that is incorrect because it is local standard time, measured from your location. Then we only have to correct for 6 hours, and at a rate of 2 hours a month, the star would be on our meridian 3 months after the vernal equinox. This would be around June 20th, not August 20th like I originally found.
From this I see you getting and not getting LST. The first half is absolutely correct, it was just the definition. The second half, well let's look...
ReplyDeleteLST is Local Sidereal Time, the sidereal time locally. This is the key to why you are off by 1 month (2hrs LST). The key things to remember are, LST advances ahead of regular times at a rate of 4 min/day = 2hr/mo. The 2hr/mo is the most useful to remember.
The way to think about this is
On Mar 20, the LST at noon is ~0hr, at midnight is ~12hr
18hr RA is 6 hrs later,
6hr ~ 6/2 = 3 mo
Mar 20 + 3mo = June 20.
I think you overcorrected by attempting to use LST in Greenwich with the zero still set to Cambridge.
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ReplyDeleteI am still confused, wouldn't that give the date that the star is on the meridian of Greenwich, not Cambridge?
ReplyDelete