ASTR 1110 Lecture #2: Deep Distance and Deep Time Tuesday, June 6 2000 Dr. Henry Throop / University of Colorado Announcements: Observing sessions Tu June 13, Wed June 21, Mon June 26, Wed July 5 All at SBO except June 26 @ Walker Ranch (carpool) 9-11 PM Order of June 26 & 27 reversed -- check the web page Exponents Unit conversions Timescales Sizescales Units: ly, 10^6 km, etc. 10^x movie Generate HW #1 Colorado Model Solar System --------------------------- Main points: Space is empty! (Space is _not_ empty!) HST is 300 miles above surface of Earth It's a lot further from Earth->Mars than Earth->Moon Colder futher out Angular size Planets get further apart further from sun Planets get colder further from Sun Walking at well beyond light speed Planets are tiny tiny compared to space Most of mass of Solar System is sun -- 99% Gravity still works! Even at Pluto, Sun is strong enough to keep it in orbit Sun is much closer than any other stars -- North Pole It's all a plane: peas on a plate Pluto/Neptune: orbits cross, but like an eggbeater All circular orbits Pluto: longer orbit, since a) weaker gravity, and b) further to go Visibility: if planets behind sun, can't see them! Venus/Merc: always near sun! Thus always morning/evening objects! 1:10 billion scale Definition of AU: 150 million km (93 million mi) Spacecraft been out to Pluto's distance (not to Pluto though); people only to Moon. Big picture: This is one particular SS What's out beyond it? A: lots more plutos! Out to how far? 100's of AU? Harder to see by R^-4. Other SS's: big massive Jupiter right in at Mercury's distance! Doesn't it boil away? Scale of universe ----------------- Unit conversion -- miles per ly, etc. # of atoms in universe (more unit conversion) Scientific notation "To me, I can grasp numbers up to about a thousand. But more than that, come on. Are there a million grains of salt here, or 10 million? I mean, I got no _intuitive_ idea. I can't tell the difference. We can calculate it, and we should." Powers of 10 (1.4 10^28 cm = 15 10^9 ly; atom = 10^-10 cm) For dealing with really big numbers, or really small. Far far easier to deal with than writing 0.0000000001. Q: which is bigger? 6000000000000 or 600000000? A: one is 100x bigger than the other! Q: which is bigger? 1 10^-3 or 2 10^-5 A: first look at exponent. Write it out at first if you have to Different ways to write same value: 300 million meters/s 300000000 m/s "3 with 8 zeros after it" m/s 3 10^8 m/s 3e8 or 3d8 (programming languages) 3 EE 8 (into calculator) ** To multiply numbers in scientific notation, multiply the base (first #) and add the exponents eg: 4 10^5 x 3 10^3 = 12 10^8 = 1.2 10^9 ** To divide numbers in scientific notation, divide the base (first #) and subtract the exponents eg: 3 10^6 / 1 10^-7 = 3 10^(6 - -7) = 3 10^13 ** To add or subtract numbers in scientific notation: no easy trick, except to ignore one of the numbers entirely (if you can): eg: 10^9 + 10^2 = 10^9, for all practical purposes, since one is so much smaller than the other Careful: 10^5 is _not_ 10 x 10^5! Punch into calculator as 1 EE 5, not 10 EE 5! Most of the time in science, use most compact, most generalized form. Timescales ---------- Usually simpler: mostly measured in seconds or years from the start. 1 yr = 3.15 10^7 seconds (pi x 10^7 seconds -- just a coincidence!) UNIT CONVERSION --------------- convert 1 day into how many sec? (1 day)(24 hrs/day)(60 min/hr)(60 sec/min) = 86400 convert 1 yr into how many sec? (1 year)(365 day/yr)(24 hrs/day)(60 min/hr)(60 sec/min) = 31,536,000 = 3.15 10^7 Speed of light is how many mph? (3 10^8 m/s)(3 ft/1 m)(1 mi/5280 ft)(60 s/ 1 min)(60 min/hr) = 1 ly = (86400 s/day)(365 day/yr)(3 10^8 m/s) = 9.5 10^14 m Density of water is how much? (1 gram/cm^3)(100^3 cm^3 / 1^3 m^3) (1 kg / 1000 g) = 1000 kg / m^3 ** if the units are cubed, the number in front has to be too! Joan Baez: "... And here I sit, and on the telephone, hearing a voice I'd known, a couple of light years ago..." (Diamonds & Rust) (Respect, disc 4, track 6, 0:44 - 1:00) Difference between Galaxy, Solar System, Universe # of Atoms in Universe ---------------------- Mass of hydrogen atom = 1 10^-24 g Mass of sun = 2 10^33 g Stars in Galaxy = 1 10^11 Galaxies in Universe = 1 10^11 Atoms in universe = (2 10^33 g/star) (10^11 stars/galaxy) (10^11 galaxies/universe)(1 atom/10^-24 g) = 2e79 atoms/universe Fermi estimation: ----------------- Order of magnitude -- factor of 2, factor of 10. No decimal places, no advanced math -- it's all just 3rd grade math, multiplying numbers together. Can use calculator but really it's faster without. Astronomers have reputation for caring about details but right now we're looking at the big picture. Blades of grass on CU Campus: take a measure: 20 per inch, 400 per si, by 10^2 per sf, by 5000^2 per sm, over 2, -> 8e11 -> 1e12 (quadrillion) blades of grass. How many bricks on the campus? brick is 1' tall, 1' wide. Average building is 500' circumference, 50' high 100 buildings on campus -> (500 x 50 x 2) x 100 -> 5 million bricks, 50 million pounds (100 buildings/campus)(4 walls/building)(50 ft x 100 ft / wall)(1 brick / ft^2) = 2 million bricks How many pickup truck loads? 5 tons per load (big truck) -> 10,000 lb 50d6 / 10d3 = 5d3 = 5000 loads 3 loads/day -> 5 years of pickup truck loads to drive it all in. Problems: --------- How many stars are visible from Boulder? How many grains of sand are on the Earth's beaches? How many total mammals are there living on the Earth right now? How many used to be alive but are now dead? How many birds (dead & alive)? Insects? Bacteria? How many raindrops fall down on the Earth every day? What is the weight of the Earth's entire water (oceans, rivers, clouds)? Given these two calculations, how long does it take for an average raindrop to complete an entire cycle (clouds -> rivers -> oceans -> clouds)? Movie ----- Powers of 10