Lecture 1ASTR 1020 1st EditionGives us a larger context for our experiences and life- Tells us about our origins and historyAstrophysics –shows us how the universe works in extreme conditionsLight =main tool for astronomy Everything comes down to massCosmology –study of the universeSizes and Scales powers of 10 * scaleofuniverse.com * Math Tricks1/15Powers of 10Logarithm =10 to the power of what?X=1000=10^3 log(x)=3 / x=.0001 =10^-4 log(x)= -4Scaling Relations- Many quantities in astronomy scale work as a power of some other quantity- Luminosity is proportional to temperature to the 4th power- Fgravity = G Mm/R^2 Force of gravity F is proportional to the distance betweentwo objects R to the -2 power>Length / Area=length^2 / Volume=length^3<- If length increases 10x (10^1)- Area increases 100 (10^2)- Volume increases 1000x (10^3)if T increases 10x, L increases 10,000x (10^4) L=T^4Ex: I am twice the height of my daughter. She weighs 10kg, how much do I weigh?- Weight is proportional to volume- Volume “goes as” length cubed2x the length 2^3=8x the volume=8x the weight8 x 10kg = 80kgEx: Two ceramic frogs, with ribbons around their necks. The larger frog is twice the length of the small frog2x larger ribbon (length)4x more paint (area)8x more clay (volume)A ratio is a comparison of two numbers/ a fraction or a division of two numbers 1:3 1/3 .3333….. 33.33% **Never use more than 3-4 significant #’s in an answer in this class**- Eliminates a lot of nastiness by comparing the ratio of two quantities rather than the quantities themselvesM1 = 4pi^2/G x a3:1/p2:1 / M2 = 4pi^2/G x a3:2/p2:2 M1= a3:1 x p2:2 / M2 = a3:2 x p2:1 units cancel!(M1/M2) = (a1/a2)^3 x (p1/p2)^-2 Astronomical DistancesAU –earth-sun distance 1.5 x 10^8 kmLight Year –best for interstellar distances= distance light travels in a yearParsec -3.26 light years (explained more later)- c=300,000 km/sec =3 x 10^8 m/sec =SPEED OF LIGHTDimensional Analysis - Breaking everything into units of distance, time, mass, energy, and a few others and see how they scaleHow fat is a light year?Want: distance Have: distance/time, period of timeD= (d/t) x tLight year= speed x year=3 x 10^8 m/s x 1yearx365 days/year x 1 yearx24 hours/day x 365 days/year x 1yearx60 min/hour x 24 hours/day x 365 days/year x 1year3 x 10^8 m x 60 x 60 x 24 x 365(m)=9.46x10^15mlight year ~ 10^16 mMoon light secondSun 8.5 light minutesOuter Solar System few light hours- Speed of light means we are looking backwards in timeInterstellar scales 10^19 factor of a billion 10^9Earth’s diameter= 1.3 x 10^3km x 10^-10
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