Positional Astronomy Ch 2 1 Outline Constellations Seasons

Positional Astronomy (Ch 2) 1

Outline Constellations Seasons Coordinate Systems in General Celestial Sphere and Celestial Coordinates Precession Apparent Motions of the Sun Solar vs. Sidereal Time 2

What’s visible in the sky? • Stars: about 3000 visible at any time. • Sun: does it appear to move on the same path from day to day? • Moon: does it always look the same? • Planets: do they move relative to the stars? Are they visible every night? 3

What’s visible in the sky (cont. )? • Comets, on occasion. (Asteroids: need binoculars, or telescopes) • Meteors • Galaxies: (Small and Large Magellanic Clouds visible to naked eye, and Andromeda with binoculars) • Satellites (man-made ones) 4

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On modern star charts, all stars are contained in some constellation on the sky – here is Orion: 88 constellations officially recognized by the International Astronomical Union (IAU). But are the stars really all together in space? 6

Star patterns can help you find your way around the sky. Note: angular distance between Polaris and Spica is about 100 , so this is a big chunk of the sky. Consult the star charts in your book! 7

An asterism is a star pattern that is not classified as a constellation. 8

Why do we see different constellations at different times? • Over the night, “diurnal motion”, due to the rotation of the Earth rotates from west to east, so sky appears to rotate from east to west. Stars rise and set. • Over the year, the nighttime side of Earth gradually turns toward different parts of the sky. Orion Scorpius Not to scale! 9

Stars appear as trails due to diurnal motion. The trails are called diurnal circles. 10

In the northern sky, circles are centered on one point, close to Polaris, the Pole Star. “Circumpolar” stars and constellations never rise nor set. About how long is this exposure? 11

Seasons: what causes them? • The Earth’s axis of rotation is tilted with respect to the plane of the Earth’s orbit around the Sun. • Rotation axis inclined 23. 5° away from the perpendicular to the orbital plane. 12

=> This causes solar illumination and number of daylight hours to vary at any location throughout the year. When the Sun is higher in the sky (summer), energy is concentrated, and ground heats up. When the Sun is lower (winter), its energy is more diffuse, and ground stays cooler. Also, there are more hours of daylight in the summer, making it hotter. 13

Erroneous explanation to seasons • Some imagine seasons are caused by the Earth being closer or farther away from the Sun. • Not true, because: – When it is summer in the northern hemisphere, there is winter in the southern – The Earth's orbit is almost a circle – The Earth is closest to the Sun in January 14

Coordinate systems • Purpose: to locate astronomical objects • To locate an object in space, we need three coordinates • Either x, y, z (Cartesian), or direction (two coordinates), and distance (spherical), which makes more sense for the sky. 15

How do we locate places on Earth? • Ignoring altitude, to describe a location on the surface of the Earth we use two coordinates, measured in degrees: – Longitude – Latitude 16

• Position in degrees: – Longitude: connecting the poles, 360º, or 180º E and 180º W 0º 90º N 0º 90º S – Latitude: parallel to the equator, 0 -90º N and 090º S – A location is the intersection of a longitude and latitude line • Albuquerque: 35º 05' N, 106º 39' W 17

The Celestial Sphere • Used to describe the position of a celestial object • The Sun, the Moon and the stars are so far away that we cannot perceive their distances - no depth perception. • Instead, the objects appear to be projected onto a giant, imaginary sphere of arbitrary radius centered on the Earth. • The celestial sphere is fixed to the stars, so it appears to rotate around the Earth as the Earth rotates. • By setting up a coordinate system on this sphere, we can say 18 where to point our telescopes to find an object.

The celestial equator is the projection onto the celestial sphere of the Earth’s equator. The Earth's poles extend and intersect with the celestial sphere as the North celestial pole and the South celestial pole. To locate an object, two numbers (in degrees), like longitude and latitude are sufficient. Remember: this is not a real sphere! Radius arbitrarily large 19

The zenith is the point directly overhead. The view from our latitude: The meridian is the north-south circle that passes through the zenith and both celestial poles. The horizon delimits the portions of the sky we can and can’t see at any given time. Over the course of a night, the celestial sphere appears to rotate around us. Cardinal directions 20

Celestial Coordinates The imaginary celestial sphere is what astronomers use to define positions of objects in the sky. Angular coordinates on the sphere tell us in what direction to look to see a particular star, or galaxy, etc. Two coordinate systems worth mentioning, but astronomers only use the second one we'll talk about 21

The Horizon coordinate system • Altitude – Angle above the horizon – 0° (horizon) to 90º (zenith) – The altitude of the north celestial pole equals the observer's latitude on Earth. Meridian • Azimuth – Angle measured eastward along horizon, starting from the north – 0 -360º 22

Pros and cons of the horizon system • Pros – Easy to understand • Cons – At different position on the Earth, the same object has different coordinates – At different times, the same object has different coordinates Most telescopes need to use altitude and azimuth to point, but we need a system that avoids these drawbacks. 23

The Equatorial coordinate system • A system in which the coordinates of stars and galaxies do NOT change for observers at different locations on Earth. (Not strictly true: later). • The coordinates are called Right Ascension and Declination, and are analogous to longitude and latitude on Earth. 24 • The equatorial coordinate system is fixed to the celestial sphere.

Declination (Dec) is a set of imaginary lines parallel to the celestial equator. Declination is the angular distance north or south of the celestial equator. Defined to be 0 at the celestial equator, 90° at the north celestial pole, and -90° at the south celestial pole. Right ascension (RA): imaginary lines that connect the celestial poles. Right ascension is the angular distance eastward from the vernal equinox. RA – Dec simulator 25

Note how the Sun moves across the celestial sphere as the year goes on. It’s fixed to the stars, not the Sun. Vernal equinox is the point on the celestial equator the Sun crosses on its march north - the start of spring in the northern hemisphere (cf. Greenwich 0 longitude). More later. Vernal equinox So 0° of RA is defined as location of Sun at midday on the Vernal equinox, and location overhead at midnight on the autumnal equinox. Note Sun is at Dec=0° at these times too. 26

• Declination (Dec) is measured in degrees, arcminutes, and arcseconds. • Right ascension (RA) is measured in units of time: hours, minutes, and seconds. • This stresses that the sky is rotating over us as time passes, making changes in the sky more meaningful to observers. 27

Example 1: The star Regulus has coordinates RA = 10 h 08 m 22. 2 s Dec = 11° 58' 02" Example 2: If a star with RA = 23 h is overhead at midnight, then a star with RA = 22 h would be overhead an hour earlier. Example 3: A star with RA = 0 h is overhead at midday on the vernal equinox, midnight on autumnal equinox Example 4: In Albuquerque, our zenith is at Dec=35°, 28 and an RA that is always changing

• Caution: a star’s RA and Dec change slowly with time due to "precession" of the Earth. • Celestial coordinates are exactly right for only one instant in time. • Astronomers use "epochs", generally now 2000, to make sure everyone’s using the same reference frame! The coordinates given for Regulus are for epoch 2000. 29

Precession The direction where the Earth’s poles point isn’t always the same – the Earth is wobbling like a top. Why? Due to the gravitational pull of the Sun and the Moon on the non-spherical Earth. The Earth has an equatorial bulge – It is a little fatter at the equator than at the poles. (Diameter difference is 43 km out of 12, 756 km) 30

The gravitational pull of Sun and Moon on Earth’s equatorial bulge causes the poles to trace out a circle, like a spinning, wobbling top. This is "precession". 31

So the north celestial pole slowly traces out a circle among the northern constellations. It takes 26, 000 years to trace out one circle. Polaris won’t always be our "pole star"! Most of the time we don’t have one! Thus RA and Dec coordinates, which are tied to the positions of the celestial poles and celestial equator, change slowly with time. 32

More on Sun’s apparent motion as seen from Earth The ecliptic • Because of the tilt of the Earth's rotation axis, over the year the Sun seems to travel on a path on the celestial sphere which is tilted 23. 5° with respect to the celestial equator. • This path is called the ecliptic. 33

It appears to us that the Sun travels around the celestial sphere once a year. A parallax effect: as we orbit Sun, it is projected against different stars. After 1 year, it returns to same position relative to the stars. 34

Solstices and Equinoxes In March, the Sun moves northward across the celestial equator - at the vernal equinox (recall this defines 0 h RA). In September, the Sun moves southward across the celestial equator - at the autumnal equinox. Day and night have equal length on equinoxes. The summer and winter solstices occur at the northernmost and southernmost points of the ecliptic. Path of the Sun over the year Ecliptic Simulator 35

Apparent path of the Sun over the day at different times of year 36

Change in length of day at high latitudes is quite dramatic! Above Arctic Circle, Sun never sets for some days in summer. 37

Solar vs. Sidereal Time • In "real life", we use the Sun to tell time – it defines the length of a day. • A solar day is the time interval between successive meridian crossings of the Sun – noon-to-noon. • This is different from time kept by the stars, known as sidereal time. • A sidereal day is the time for Earth to spin 360° on its axis. Why is this different? 38

The Earth is not only spinning but also orbiting around the Sun. The Earth must turn a bit more than 360° in a solar day because it’s moved in its orbit a little while spinning. The difference is about 3. 9 minutes. Solar day: 24 hours. Sidereal day : 23 hours, 56 minutes, 4. 091 seconds. After 1 year, Sun returns to same position on celestial sphere. A year has one fewer sidereal days in it. Useful fact for observing: sidereal time zero is defined as when vernal equinox (RA=0 h) crosses meridian. Happens at midnight on Sept 22 or midday on March 21). So in general an object crosses the meridian when the sidereal time is equal to its RA. And sidereal time=solar time on midnight, Sept 22. Observatories use sidereal clocks! 39

The Zodiac • As the Sun moves along the Ecliptic it passes through 12 constellations known as the Zodiac simulator 40

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Example 2. 29 September 21: Cygnus highest in the sky at 8: 00 PM and Andromeda at midnight. July 21: Cygnus highest at midnight. At approximately what local time is Andromeda highest in the sky? 42

Positional astronomy revisited • You are not required to know all the following details for the exams… but hopefully you will understand the relation between horizontal and equatorial coordinates. • Problem: I've got the RA and Dec coordinates for my favorite object, but where is it really on the sky tonight? 43

The easy way • Find a close constellation that you can easily recognize. • Estimate the offset in degrees from your favorite source. • Use the telescope dial (or your hands and fingers) to locate your source on the sky when you have identified the constellation. 44

The accurate way P = North Pole Z = zenith X = location of object a = RA d = Dec A = azimuth a = altitude = observer's latitude 45

Given , we have H = LST-RA (in hrs), convert H to degrees (multiply by 15). Now we want azimuth A and altitude a. The cosine rule: 
 cos(90°-a) = cos(90°- ) + sin(90°- )cos(H)
 which simplifies to: 
 sin(a) = sin( ) + cos( )cos(H) The sine rule: 
 sin(360°-A)/sin(90°- ) = sin(H)/sin(90°-a)
 which simplifies to: 
 -sin(A)/cos( ) = sin(H)/cos(a) sin(A) = - sin(H) cos( )/cos(a)
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A quicker way • The Hour Angle (HA) defines how long time ago an object passed the local meridian. • We define Local Sidereal Time (LST) to be 0 hours when the vernal equinox is on the observer's local meridian. 
 • One hour later, 
the HA of the equinox is +1 h, 
and the LST is 1 h. • Realize that an object passes your meridian when the local sidereal time = RA of object. 47

Example • The star Vega has the following equatorial coordinates: RA 18 h 36 m 56. 3 s Dec +38° 47' 1" • Where can I see it on the sky tonight (Sep 4) at 9 PM? 48

Recommendations • Use a computer software program, either something that comes with your telescope or something separate • Use the Astronomical Almanac, or similar 49

Distance and Brightness Distance to Deneb 3230 light-years Distance to Vega 25 light-years Distance to Altair 168 light-years But they appear almost as bright Deneb must be intrinsically very luminous. 50