Question

Locate the star Betelgeuse and click on it. Information on Betelgeuse should appear in the top left of your screen. What is its azimuth and altitude?

Az (1 pt) = ________________
Alt (1 pt) = ________________

Now let’s switch to a different coordinate system. Press “E” or click on the globe in your bottom menu bar to turn on some new coordinates, and press “Z” or click on the radar icon (to the right of the globe) in the menu bar to turn off the altitude and azimuth grid.

This new grid should be tilted relative to the horizon. You are now looking at the Right Ascension (RA) / Declination (DE) coordinate system. This system is very similar to longitude and latitude on the Earth. If you look to the north, you will see that the lines converge near a moderately bright star. This is Polaris, the North Star. Its declination is +90 degrees, just like Earth’s north pole has a latitude of +90 degrees. If we could see through the ground, the grid would converge again in the south at declination –90 degrees; this spot would be directly over the Earth’s south pole.

If you look at the RA/DE coordinates of Betelgeuse, you will notice that RA is given in units of “h m s”. These stand for “hours”, “minutes” and “seconds”. There are 24 hours in one full circle (so each hour of RA is 15 degrees of angle), 60 minutes in one hour, and 60 seconds in one minute. (We astronomers have our nefarious reasons for using this arcane system, but it isn’t important for now.)

What is the RA and DE of Betelgeuse (to the nearest degree ignoring arc mins and arc secs)?

RA (1 pt) = ________________
DE (1 pt) = ________________

For Betelgeuse, record both its Az/Alt coordinates and RA/DE in the table below (record all values should be to the nearest degree, i.e., don’t include the arc mins and arc secs). Keeping the time at 22:00, record the new positions for the dates specified. Note that even when the star dips below your viewing horizon (alt < 0°), its position is still displayed. Continue to advance in four-month increments for an entire year (for time 22:00 at each date). (1 point each totaling 16 pts)

Date   Az   Alt   RA   DE
2019-01-28        

     
2019-05-28              
2019-09-28              
2020-01-28              

Using the answers above answer the following:
Which coordinates change (1 pt)?
Which remain the same (1 pt)?
Do the changing coordinates ever come close to repeating (1 pt)?
If so, after roughly how long (1pt)?

Next, keeping the time, date, and location the same, find Polaris. What is the altitude of Polaris to the nearest degree?

Let’s go somewhere else on the Earth. Open the Location Window (see point 1 at the start of the lab) and type “Greenwich” into the search box. Select the “Royal Observatory (Greenwich), United Kingdom” from the list. Change the date and time to 2019-01-27 at 03:00PM (15:00) – this accounts for the 6-hour difference in time between Texas and England (your clock is showing Dallas time even though you changed positions).

Answer the following for Betelgeuse:
What are the Az/Alt (1pt)
What are the RA/DE? (1 pt)
Compare answers for a and b to the first row in your table for 3. Which numbers are different? (1 pt)
Which are the same? (1 pt)

Let’s say you are studying a new star and you need to get some pictures soon. You email all your friends who are at big telescopes, since it doesn’t matter from which telescope, nor what time of night you get the pictures.
Should you send your friends the star’s current Az/Alt or its current RA/DE? (1 pt)
Why? (1 pt)

What is the altitude of Polaris as seen from Greenwich (to the nearest degree)?

Polaris is used in navigation because of the fact that its altitude is always the same as the latitude of the observer. Using your answers for the altitude of Polaris from Dallas and Greenwich, how do these values compare with the latitude of those locations?

Part III: Sunrise and Sunset

We all know that the sun rises in the east and sets in the west, right? Let’s examine the position and time of the rising and setting sun over the course of the year, and see how true that is.

Toggle back to Az/Alt coordinates (press Z) for this exercise, and return your location to Dallas, United States. (and make sure to check the enable daylight savings time in the location screen) Use the arrow keys to look toward the eastern horizon.

Set your date for 2019-01-21 and change the time until you see the sun. Click on the sun to get its coordinates. Then change the time of day until the sun has an altitude as close as you can to 0 degrees, 0 arcminutes, and 0 arcseconds. Since its altitude is zero, this means that the sun is just starting to rise in the east. Get the altitude as close as you can, but because you cannot adjust time in smaller than 1 second increments, understand that you will probably not be able to get an altitude of precisely 0°0’0”. (Note that with the online version of Stellarium, the coordinates do not update with each time change unless you re-select the Sun with each time change).

Find the sunrise and sunset times, and the positions to the nearest degree, i.e., don’t include the arc mins and arc secs) on the dates specified and fill in the table. Note to be sure to turn on the setting to account for daylight savings time. (1 pt each, or 16 total pts)

Date   Sunrise   Sunset
    Time   Az   Time   Az
2019-09-21               
2019-12-21              
2019-03-21              
2019-06-21              

What azimuth values correspond to precisely East and West?
East azimuth: _____________________ (1 pt)
West azimuth: _____________________ (1 pt)

Which dates does the sun rise/set on these azimuths?

On which day does the sun rise farthest to the north (smallest azimuth)? (1 pt)

Calculate the length of the day for each of the dates. Which date has the longest daytime?

Answer 1

SOLUTION:-

The Azimuth and Altitude of Betelgeuse from Dallas Texas on 4th February 2019 0210 hours are as follows:

Az = 256.9^o

Alt = 19.8^o

The Right Ascension and Declination of Betelgeuse from Dallas Texas on 4th February 2019 0210 hours are as follows:

RA = 5h55m

DE = 7^o

The below table shows the position of Betelgeuse in two coordinate systems as viewed from Dallas, Texas at 2200 hours

Date	Az	Alt	RA	DE
2019-01-28	186.2o	64.5o	5h55m	7o
2019-05-28	285o	-9o	5h55m	7o
2019-09-28	56.8o	-29.9o	5h55m	7o
2020-01-28	185.2o	64.5o	5h55m	7o

The Azimuth angle and Altitude coordinate system change with time.

The Right Ascension and Declination angle coordinate system remains the same.

The changing coordinates Az/Alt do come close to repeating.

They do so, approximately after one year cycle i.e. a period of 12 months.

The altitude of Polaris on 2019-01-28 at 2200 hours as viewed from Dallas, Texas is 33.2^o.

The location of Betelgeuse from Greenwich on 2019/01/27 at 1500 hours is as follows:

Az = 79.8^o

Alt = 1.4^o

RA = 5h55m

DE = 7^o

From the comparison, it is found that the Azimuth angle and Altitude are different for Betelgeuse when viewed from Dallas, Texas and Greenwich.

The Right Ascension and Declination are same from both Dallas, Texas and Greenwich for Betelgeuse

I should send the star's RA/DE to my friends.

The reason is because RA/DE is the same for a particular star regardless of the position of the earth they are viewed from.

The altitude of Polaris on 2019-01-27 at 1500 hours as viewed from Greenwich is 52^o.

The altitude of Polaris from Dallas, Texas and Greenwich show that their value is very close to their respective latitudes on the earth.

Part 3

Date	Sunrise(hours)	Az	Sunset(hours)	Az
2019-09-21	0717	89o	1920	271o
2019-12-21	0730	118.4o	1722	242o
2019-03-21	0735	89.5o	1935	270.4
2019-06-21	0625	62o	2033	298

East Azimuth = 90

West Azimuth = 270

On 2019-09-21 and 2019-03-21, sun rise/set on these above azimuths.

The sun rises farthest to the north on 2019-06-21.

Length of the day for each dates are as follows:

2019-09-21 = 12h03m

2019-12-21 = 09h52m

2019-03-21 = 12h00m

2019-06-21 = 14h08m

The longest day time is on 2019-06-21.

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