Some say the world will end in fire, Some say in ice. From what I've tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To say that for destruction ice Is also great And would suffice. Robert Frost, Fire and Ice

Assignments: Problem Set #8 due Tuesday 27 April, 5:00 pm Observing Lab #3 due Tuesday 27 April, 5:00pm Note: Final Exam is on 6 May at 8am in Olin 268

In Class: The Future ????? ------------------------------------ What happens next? when the universe was small, nuclear reactions were important now that the universe is large, nuclear reactions don't happen that much anymore - important universe-evolving agent must be long-range - have influence over big scales - since stuff is scatterred about - the best long-range force we know about is gravity - creates an attraction between all objects of mass in the universe (energy, too) - pretty weak to start with - you and I aren't pulled toward each other (though you and the Earth are) - gets weaker with distance - F goes as 1/r^2; "inverse square" - BUT it never disappears Its influence on the universe is the exact opposite of the Big Bang - Big Bang pushed everything outward; expansion - gravity seeks to pull everything inward - which will win? - Big Bang was very powerful - expansion was rapid and continues today - but the motivating force (the "Bang") has passed - gravity is wimpy in strength - doesn't pull hard enough to overcome expansion i.e., gax still separate - but gravity doesn't give up -- _ever_ How to figure out which will win: gravity's pull depends on mass, so - how much mass is in the universe? Consider a slingshot - shoot a ball straight up - the ball has a certain amount of energy - depends on how hard you threw it - you may remember K = 1/2 m v^2 energy = 1/2 x mass x speed^2 - however, it costs energy for the ball to go upward against the force of gravity - just like pulling against a spring - or a car going up hill - how high will the ball go? - it will go upward until it runs out of energy - then it will stop going up, and fall back down - lots of energy --> really high - not so much --> not so high - can you shoot a ball free of the Earth's gravity? - sure, if you give it enough energy - because gravity's pull is weaker the farther away you are, it takes a finite amount of energy to break free. Energy required = GMm/r <--"r" is starting point - combine these two energy expressions to find out just how fast the ball must be going to break free 1/2mv^2 = GMm/r v^2 = 2GM/r v = sqrt(2GM/r) this is "just enough"; if we give the ball more energy, it breaks free less, and it falls back to Earth called the "escape velocity" -- we saw this before in talking about photons getting out of black holes Consider the universe analog one galaxy is trying to "break free" from its neighbor - if it does --> galaxies will continue to separate forever universe will keep expanding forever Big Bang wins - if it can't -> galaxies will collapse back together universe will recollapse gravity wins Let's apply the same ideas we did with the ball and the Earth Energy of part flying away: 1/2 mv^2 - but what is the speed of this galaxy? Hubble Law v = Hd - so Energy = 1/2 mH^2 d^2 energy required to "break free" = GMm/d Equating these energies 1/2 m H^2 d^2 = GMm/d 1/2 H^2 d^3/G = M - eg "critical mass" for the nearby galaxy - if the galaxy has a mass greater than this, our galaxy won't escape, and like the ball, it will fall back toward the other gax - if the galaxy has a smaller mass, gravity isn't strong enough, and our galaxy "escapes" We don't just want to know whether these two gax will crash back together, but in general , whether the whole universe will expand forever, or collapse back on itself - don't want to have to look at each galaxy pair individually - instead, let's consider the density of the universe mass/volume in our case, if the galaxy is alone density = (mass of galaxy)/(4/3 pi d^3) - the above equation can be rewritten, 1/2 H^2/G d^3 = M and then, multiplying by 4/3 pi on both sides, 1/2 H^2/G 4/3 pi d^3 = 4/3 pi M put the M and the 4/3pi d^3 on the right hand side 1/2 H^2/G = 4/3 pi (M)/(4/3pi d^3) move the extra 4/3 pi over to the left side 3 H^2/(8 pi G) = density This is the "critical density" of the universe - concept which can apply to the whole universe - if the density of the universe is greater than the critical density, there's enough mass in the universe and gravity will win - universe will stop expanding, and collapse - behave just like the ball thrown up from the Earth without enough energy --> the Big Crunch - hot reverse of the Big Bang - death by fire - if the density of the universe is less than the critical density the universe will continue to expand - may slow down a bit because of gravity - but won't stop expanding and won't collapse - stuff will continue to get farther apart - universe will continue to cool - stars will eventually burn up all of the H in the universe - burn out --> death by ice Observational evidence suggests that we live in an "open" universe - density is less than the critical density - can't really be sure, though, because of dark matter - if dark matter exists, there could be enough of it to "close" the universe - ie, make the density higher than the critical density