AnnouncementsLectures on the course web page.

No “Lab” Wednesday in Kemper 204 – IRTF observing instead

HW 1 posted on course web page.

Continuing with RA and Dec…

MON: Now to what we really want.

If you see a star in the sky, you can determine what the RA and Dec are.

How?

By converting your local time and coordinates to RA and Dec.

Meridian Diagram: Steps 1) The latitude of the observer is the

declination of the observer's zenith. 2) The missing angle is 90 – altitude 3) Determine the declination by adding (or

subtracting) the missing angle to the declination at zenith. If you go south subtract, if you go north add.

Some rules to help

Right Ascension (RA)Tied to the seasons. 4 special points!Always work from NOONDetermine RA for NOON of the closest special

date: VE, AE, SS, WS.Do months first: Add (subtract) 2 hours per

month after (before) the special date.Then hours in the day. Add (subtract) 1 hour

per after (before) noon.

Example 1

It is midnight of the Summer Solstice and you are in Mexico (latitude=+10 degrees), you

see a star due north at an altitude of 75 degrees.

What's the RA and Dec for that star?

Example 2

It is midnight of the Vernal Equinox. You see a star at an altitude of 25 degrees above your southern

horizon. What's the RA and Dec for that star?

The Sun's motion in our sky

Declination: At both equinoxes, it is directly above Earth's

equator, so its declination is 0 degrees At the summer solstice, it is as far north as it can

get: 23.5 degrees At the winter solstice, it is as far south as it can get:

-23.5 degrees.Right Ascension: Since the Sun is always on our

meridian everyday at noon, you only need to know the date to get its RA

If you took a picture of the Sun everyday at the same

time, this is what you would get.

It is called an analemma.

Example 3

It is noon on the Vernal Equinox and (with a telescope) you see Venus 5 degrees due

South of the Sun. You are at the Equator.

What's the RA and Dec for Venus?

What is Venus' altitude?

Converting from RA/Dec to Alt-Az

•There are mathematical expressions we will use.

•But we have to get into time to do this.

Time.

•Because the Earth is spinning and orbiting (but mostly because of spin), where a star is in our sky depends on the time of day and day of

the year.

Universal Time.

•This is the same as Greenwich Mean Time.•No daylight savings time.

•Currently, UT is 5 hours ahead of us.

•Because of daylight savings time, even clocks in England are off by an hour except between

November and March.

Convert to fractional days

•Divide the minutes by 60 and add to the hours.•Divide the hours by 24.

Days since J2000.0• Days since beginning of the year:• Month: Normal yearLeap year• January 0 0• February 31 31• March 59 60• April 90 91• May 120 121• June 151 152• July 181 182• August 212 213• September 243 244• October 273 274• November 304 305• December 334 335

Days since J2000.0

•Days since beginning of the year:•Or you can use the formula:

•int(Day) = 275*(M/9) – 2*((M+9)/12) + D -30•But it doesn't count February 29 ever.

Days since J2000.0

•Then account for days at the beginning of each year since 2000:

•Year:Days: Year: Days:•2000 -0.5 2015 5477.5•2010 3651.5 2016 5842.5•2011 4016.5 2017 6208.5•2012 4381.5 2018 6573.5•2013 4747.5 2019 6938.5•2014 5112.5 2020 7303.5

Days since J2000.0

What is the day number for 15:30 UT on April 4, 2010?

What is the day number for 2PM CDT on Sept. 2, 2011?

Sidereal versus Solar

•But because we are orbiting the Sun, a solar day is not the same as a day according to the

stars.

A solar day is one full rotation

according to the Sun.

A sidereal day is one full rotation according to the

stars.

Because the Earth is in motion around the Sun, it takes longer

for the Sun to get back to the same position in

our sky.

So a sidereal day is nearly 4 minutes

shorter than a solar one.

Mercury is really freaky!

1 sidereal day = 59 Earth days,1 solar day = 176 Earth days,

1 orbit = 88 Earth days.

Sidereal time

•If we have solar days and sidereal days, then we can have solar time and sidereal time.

Sidereal time

•Sidereal time is time according to the stars.•And in a standardized way, it corresponds to

the same longitude as UT (Greenwich).

•So if you're at Greenwich and it is 4am sidereal time, then stars with an RA=4 are on

your meridian.•If it's 10pm, then stars with an RA=22 are on

your meridian.

Sidereal time

•But just like we don't set our house clocks to GMT, we usually local sidereal time (LST). In that way, stars on our meridian at any time

have the same RA as LST.

Local Sidereal Time

•We can calculate LST using the formula:•LST = 100.46 +0.985647 * d + long + 15*UT

•This gives LST in degrees (0 - 360). •To get LST in hours, divide by 15.

•This formula is accurate to 0.3 seconds within a century of J2000

Local Sidereal Time

•LST = 100.46 +0.985647 * d + long + 15*UT•Example: What is LST for 23:10 UT, August 10, 2000 at Birmingham UK (long: 1'55 W)?

Local Sidereal Time

•Another formulation (if you like this any better)•LST = 280.46061837+360.98564736629 * d + long

•Note that this will give you a huge number! You then have to correct it by factors of 360 until the answer is

between 0 and 360 degrees.

Local Sidereal Time

•LST = 100.46 +0.985647 * d + long + 15*UT•Example: What is LST for here, now (1:45PM CST).

•Our longitude = 93o17'10”W

Hour Angle

•Hour angle is the East-West angle between the meridian and an object in the westerly direction.

So it is the time since an object passed the meridian.

•It is usually measured in hours (like RA), but for the conversion between Alt-Az and equitorial

coordinates, it will need to be in degrees.

• HA = LST - RA

Hour Angle

•In more common usage: It is the angle between an object and the meridian (East or

West, whichever is closest).

•HA = LST - RA

Hour Angle

•But for this exercise, we will use it as the distance going West from the meridian, in

degrees.

•HA = LST - RA

Hour Angle

•So what is the HA for a star with RA=14:32:27 at LST=19:52:48?

•HA = LST - RA

Hour Angle

•So what is the HA for a star with RA=8:32:27 at LST=3:18:26?

•HA = LST – RA

Conversions!!!

•Now we have all the terms needed to convert RA (HA really) and Dec to Alt-Az

coordinates.

•So given RA and Dec, you can now convert to Altitude and Azimuth.

Convert from RA/Dec to Alt-Az

If sin(HA) is negative, then Az = A; otherwise, Az = 360 - A.

Convert from RA/Dec to Alt-Az

If sin(HA) is negative, then Az = A; otherwise, Az = 360 - A.

NOTE that RA and LST are inside of

HA.