What is astronomy? Greek word astronomia Asteri = star Nomos = law, principle, act The study of the cosmos (at all scales). What scales are relevant to astronomy?

Part of studying cosmos is understanding where we are in it Part of studying cosmos is understanding where we are in it. Our context. 10-8 m

How astronomy works In astronomy, we make observations and measurements: Angles, Motions, Morphologies, Brightnesses, Spectra Etc. We interpret and explain in terms of physics: Mechanics, atomic and molecular processes, radiation properties thermodynamic properties, etc. Through which we learn about nature and history of the cosmos: Structure and evolution of stars, galaxies, galaxy clusters, origin and expansion of the universe Our theories in turn motivate the next observations, thus our understanding is continually being refined.

Angles, Powers of Ten, Units in Astronomy

Angles Astronomers use angular measure to describe: the locations of celestial objects on the sky the apparent size of an object separation between objects movement of objects on the sky (later: to convert to actual sizes, separations, motions, must know distance to object!)

A circle is divided into 360 degrees The Moon subtends about half a degree Another way of saying this: the Moon has an angular diameter of half a degree. The Sun subtends about the same angle.

How to estimate angles Extend your arm, and use your hand and fingers like this: Is this what you expected for the Moon’s angular diameter?

Example of angular separation: the “pointer stars” in the Big Dipper

How do we express smaller angles? We subdivide the degree into 60 arcminutes (a.k.a. minutes of arc): 1 = 60 arcmin = 60’ An arcminute is split into 60 arcseconds (a.k.a. seconds of arc): 1’ = 60 arcsec = 60” An arcsecond is split into 1000 milli-arcseconds (yes, we need these) We need much smaller angles in astronomy.

The small-angle formula Relation between angular size, physical size, and distance to an object: where D = linear size of an object = angular size of the object (in arcsec) d = distance to the object (in same units as D) Derive from s=r x theta 206,265 is the number of arcseconds in a circle divided by 2 (i.e. it is the number of arcseconds in a radian). Where does this formula come from?

The same idea in pictures: the angular size depends on the physical, linear size AND on the distance to the object. See Box 1-1. Objects can be of very different linear, physical sizes, but still have the same *angular* size, because they are at different distances from the observer. Derive from s=rtheta.

Examples The Moon is at a distance of about 384,000 km. If it subtends 0.5°, from the small-angle formula, its diameter is about 3400 km. Do calculation and show use of approximation. Point out we use metric system The resolution of your eye is about 1’. What length can you resolve at a distance of 10 m?

Powers-of-ten notation Astronomy deals with very big and very small numbers – we talk about galaxies AND atoms! Example: distance to the Sun is about 150,000,000,000 meters. Inconvenient to write! Use “powers-of-ten”, or “exponential notation”. All the zeros are consolidated into one term consisting of 10 followed by an exponent, written as a superscript. Eg., 150,000,000,000 = 1.5 x 1011

Examples: powers-of-ten notation 150 = 1.5x100 = 1.5 x 102 84,500,000 = 8.45 x 107 10-2 = 1/102 = 1/100 0.032 = 3.2/100 = 3.2 x 10-2 0.0000045 = 4.5 x 10-6 Conversly, the exponent tells you how many times you have to multiply 10 together to get the number.

Arithmetic with powers-of-ten notation To multiply numbers, add exponents: Examples: 10x100 = 101x102 = 1000 = 10x10x10 = 103 (2 x 104) x (3 x 105) = (2 x 3) x 104+5 = 6 x 109 To divide numbers, subtract exponents: Example: (6 x 106) / (3 x 104) = (6/3) x 106-4 = 2 x 102

Some familiar numbers in powers-of-ten notation: prefix One thousand = 1000 = 103 kilo One million = 1,000,000 = 106 mega One billion = 1,000,000,000 = 109 giga One one-hundredth = 0.01 = 10-2 centi One one-thousandth = 0.001 = 10-3 milli One one-millionth = 0.000001= 10-6 micro

Important note on Significant Figures A significant figure is any digit in a number when it is written in scientific notation. For example, 3.14159 = 3.14159 x 100, has six significant figures but so does 0.0000314159 = 3.14159 x 10-5. 2.850 has four significant figures, but 2.85 has only three. The last zero is telling you that that digit is not 1 or something else, but 2.85 could be representing 2.851, rounded off. It is important in calculations to keep only significant figures, e.g. 1.2/1.1 = 1.1, even though calculator says 1.0909090909090909…, the input numbers were only know to 1 sig fig, so the answer is too.

Units in astronomy Every physical quantity has units associated with it (don’t ever leave them off!). Astronomers use the metric system, distances in meters masses in kg time in s temperature in °C or K and a few special units (see later).

Size estimate Atom: 10-8 m

Size estimate Child: 100 m

Size estimate Earth: 107 m

Size estimate Sun: 109 m

Size estimate Galaxy: 1021 m

Size estimate The visible Universe: 1026 m

Special distance units: light-year A light-year is the distance the light travels in one year. Speed of light is 3 x 108 m/s. In one year, light travels about 9.5x1015 m. Example, light takes 4.22 years to travel from Earth to Proxima Centauri, the nearest star beyond the solar system => Proxima Centauri is 4.22 light-years away. Hence we see this star as it was 4.22 years ago. NB: a distance, not a time. Calculate number of seconds in a year.

The visible Universe If the Universe is 13.8 Gyr old, we cannot know anything about objects for which the light would have had to travel more than 13.8 billion light-years to get to us (those signals have not yet had enough time to reach us) R~13.8 billion lyr …all objects whose light has traveled less than 13.8 billion light-years to reach us.

The Astronomical Unit (AU) 1 Astronomical Unit = 1 AU = the average distance between the Earth and the Sun = 1.496 x 108 km. Why? It’s convenient for interplanetary distances! Example: The average distance between Jupiter and the Sun is 5.2 AU. Isn’t that simpler than 7.8 x 108 km ?

Mercury: 0.39 AU Venus: 0.72 AU Earth: 1.00 AU Mars: 1.52 AU

The parsec Short for "parallax of one second of arc" It is the distance to a star which has a “trigonometric parallax” of 1", when observed at two opposite positions in the orbit of the Earth around the Sun, taken 6 months apart. If the trigonometric parallax is p, then d (pc) = 1/p (arcsec) Note: diagram not to scale!!! Can understand size of pc in AU from small-angle formula. Show this. Small angles: assume both long sides of triangle equal because star so far away. 1 pc = 3.1 x 1016 m = 206,265 AU = 3.3 light years