1	Astro 1050 Lecture 2 A Little More about Scientific Notation, Units, and the Scale of the Universe How we name and start to classify stars Constellations, Magnitudes How the stars move across the sky The celestial sphere
2
3
4
5	Scientific Notation 10¹= 10 10²= 100 10³= 1,000 (one thousand) 10⁶ = 1,000,000 (one million ) You can think of this as raising 10 to some power – or just think of it as moving decimal place over some given number of steps. Think of computer speeds and disk space. 10⁰ = 1 10^-1= 0.1 = 1 / 10 10^-2= 0.01 = 1 / 100 10^-3 = 0.001 = 1 / 1,000 10^-6 = 0.000001 = 1 / 1,000,000 How to write numbers which are not powers of 10: 1 A.U. = 149,597,900 km = 1.496 ´ 10⁸ km = mantissa ´ 10^exponent
6	Arithmetic and Scientific Notation Multiplication: Multiply the mantissa Add the exponents 20 AU = (2 ´ 10¹)´ (1.496 ´10⁸ km) = (2 ´ 1.496) ´ (10¹ x 10⁸) km = 2.9992 ´ 10⁹km Division: Divide the mantissa Subtract the exponents 1 AU / 500 = (1.496 ´10⁸ km) / (5 ´ 10²) = (1.496 / 5 ) ´ (10⁸ / 10²) km = 0.2992 ´ 10⁶ km = 2.992 ´ 10⁵ km Be careful when adding or subtracting: (2.0´10⁶⁾+ (2.0´10³) = 2,002,000 = 2.002´10⁶ not 4. ´10⁶
7	Scientific notation and the metric system
8
9	A light-year: Distance Not Time! speed of light = c = 3.0 ´ 10⁸ m/s distance = speed ´ time d = c ´ t light-second = 3.0 ´ 10⁸ m/s ´ 1 s = 3.0 ´ 10⁸ m light-minute = 3.0 ´ 10⁸ m/s ´ 60 s = 180 ´ 10⁸ m = 1.8 ´ 10¹⁰ m light-year = 3.0 ´ 10⁸ m/s ´ 3.14 ´ 10⁷ s (i.e. 31.4 million s) = 9.4 ´ 10¹⁵ m = 9.5 ´ 10¹² km = 9.5 trillion km = 9,500,000,000,000 km
10	Example of using Units as a check If someone says: “The time it took me to walk to class today was 10 minutes.” the number could possibly be wrong, but the statement at least makes sense. If someone says: “The time it took me to walk to class today was 10 kilograms.” something is obviously wrong. When you use a formula to calculate some answer – you can treat units just like numbers – multiplying and canceling them. The units you are left with MUST be those which match the ones expected – or you have made some mistake.
11	Another example of Units, with conversions 1 light-year = c ´ t (where c is the speed of light and t is one year) = 3.0 ´ 10⁸ m/s ´ 365 days = 1.1 ´ 10¹¹ (m ´ days /s) but we know light-years is a distance and must have “dimensions” of distance. We should have units of just meters. The fact that we have this extra (days/s) means we have left something out. If we multiply by (24 hr/day ´ 60 min/hr ´ 60 sec/min) the units will work out right and so will the numerical answer = 1.1 ´ 10¹¹´ 24 ´ 60 ´ 60 m = 9.5 ´ 10¹⁵m = 9.5 ´ 10¹² km
12	"Chapter 2:" Chapter 2: The Sky Constellations: -Originally vague -Mostly Greek -Now well defined -Total of 88 Asterisms: -Less Formal Groups
13	Big Dipper The stars in a constellation or asterism like the Big Dipper are NOT necessarily at the same distances. These are just chance arrangements as seen from Earth.
14	Names of stars Proper names mostly from Arabic Astronomers use (a, b, d, e, ... ) + Constellation in approximate order of brightness Alpha Orionis = Betelgeuse Beta Orionis = Rigel Alpha Tauri = Aldebaran Numbers and other schemes for fainter stars. (About 6000 stars are visible to naked eye.)
15	Magnitudes (m) to denote brightness Ancient system created by Hipparchus 1^st magnitude = brightest stars in sky 6^th magnitude = faintest visible to naked eye Confusing because smaller number implies brighter (Think of first magnitude as “first in class”) Astronomers want a numerical measure of Intensity (I) which is proportional to energy per unit time received from the star. Relationship between I and m turns out to be “logarithmic” (result of properties of human eye)
16	Numerical Relationship between m and I Every increase in m by 1 is a drop in brightness by a factor of 2.512 We receive 2.512 times less power from a 2^nd magnitude star than from a 1^st magnitude one. We receive 2.512 ´2.512 = 6.310 times less from a 3^rd magnitude than a 1^st magnitude We receive (2.512)⁵ times less from a 6^th magnitude star than a 1^st magnitude. The 5 comes from 6-1. Because (2.512)⁵ = 100 (not by accident) the faintest stars we can see are 100 times fainter than the brightest.
17	Apparent Visual Magnitude Scale From our Text, Horizons by Seeds
18	Formula for I vs. m
19	The View From A Rotating Platform Imagine being being in a rotating restaurant on top of a tall building. All the outside objects are very far away – much farther than the distance across the room. Paint the view on the windows – and keep the people near the center of the room – away from the windows themselves. Can the people tell if the room is rotating, or if the painted windows are just moving around the room? Which is more reasonable – a rotating room or rotating painted windows?
20	The Celestial Sphere If you “paint” the stars on a sphere much bigger than the earth, then you can obtain the motion of the stars by pretending that sphere rotates, rather than the earth. For most people that motion is easier to “see”. The sphere rotates once every day (actually once every 23^h 56^m for reasons we’ll see later) We will see later that the sun, moon, and planets move slowly along the sphere relative to the stars. You can think of them (for a night or so) as “stars” which move almost with the other fixed – but drift relative to them from night to night. The celestial sphere will also have marked on it a projection of the earth’s latitude and longitude system, as well as a few other special points and circles.
21	Celestial Sphere
22	Nomenclature HORIZON: The horizontal circle which separates the part of the sky visible to you and the part of the sky hidden by the earth. ZENITH: The point on the sky directly overhead. MERIDIAN: The circle which starts on the northern horizon, runs through the zenith, continuing on to the southern horizon. It separates the eastern half of the sky from the western half. CELESTIAL POLES: The points where the extension of the rotation axis of the earth would intersect the celestial sphere. CELESTIAL EQUATOR: The circle around the sky which would be a projection of the earth’s equator.
23	Limiting Cases At the Earth’s north pole, looking overhead all stars appear to circle around the north celestial pole. At the equator: Stars on the celestial equator rise in the east, move overhead, then set in the west The N and S celestial poles are just on your N and S horizons, and stars near those points still circle around them. But those stars are only visible for the upper half of their circles.
24	Intermediate cases like Laramie Stars close enough to the north celestial pole are always above the horizon, and just circle the pole star. (CIRCUMPOLAR STARS) Stars on the celestial equator rise in the east, move higher along a slanted path which crosses the “meridian” to the south of the zenith, then descend and set due west. Stars far enough to the south never make it above the horizon.
25	Star Motion from the Northern Hemisphere
26	Precession of the Earth The earth’s axis of rotation is tilted 23.5⁰ relative to the plane containing the sun and other planets. The gravity from the Sun and moon is trying to tip the earth just like gravity is trying to tip a spinning top. As with the top, the axis of the earth wobbles or PRECESSES in space, with a 26,000 year period. Because the directions to the celestial poles are defined by the spin axis – those poles move with time. It isn’t that the stars move – it is that the grid we paint on the celestial sphere has to be redrawn from time-to-time. Eventually Polaris will not be the “pole” star.
27	For Next Time…