public:courses:physics:from_big_bang_to_dark_energy:intro

# From The Big Bang to Dark Energy

• A good physicall theory should:
• Agree with observations/experiments.
• Provide an unified description.
• Be simple.
• Universal gravitation formula from Newton: $F = G \frac{M \cdot m}{r^2}$.
• We also have $F=m \cdot \vec{a}$
• When combining those two equations we can fully explain the elliptical motion of the planets.
• Earth revolves around the sun at 30km/s.
• If we consider a circular orbit approximation (which is actually not too bad), then, we have:
• $F = -G \frac{M \cdot m}{r^2}$
• The centrifuge force gives us: $F = \frac{m \cdot v^2}{r}$.
• When combining these we get the approximate orbital speed: $v = \sqrt{\frac{GM}{r}}$.
• So outer planets are moving more slowly.
• On the surface of the earth the acceleration is: $a = -G\frac{M}{R^2}$.
• In general relativity the mass doesn't really matter because is important part is rather on the curvation of space: eg. gravity seems to be an illusion from that perspective.
• When trying to compute the escape velocity for a black hole we get the result: $c^2 = \frac{2GM_{BH}}{R}$.
• For the mass of the sun we find that the limit radius as described above would be R=2.95km.
• Earth-Moon distance is 380000km (eg. 1.3 light seconds)
• Earth-Sun distance is 8.3 light minutes (eg. 1.5 10^8 km).
• Voyager is at 16 light hours (it left the solar system already).
• Our solar system is moving at 220Km/s around the center of the galaxy.
• The black hole at the center of our galaxy is 4 million times bigger than our sun.
• All the rotation curves of galaxies that we have measured so far all look pretty flat: eg the speed of revolution doesn't decrease with the distance from the center of the galaxy.
• It would seem that galaxies are surrounded by dark matter.
• See: Sloan Digital Sky Survey
• Dark ages is when we observe the universe at 13.6 billion light years : universe was too young to create a star at that time, so, there is no star at all.
• The background noise left from the big bang is actually due to light “stretched” to radio lengths. (eg. microwaves)
• This is called the cosmic microwave background (CMB).
• Age of the universe: 13.8B lyrs.
• The initials of Stephen Hawkings are written into the picture of the universe.
• The sun is getting lighter by 4 million tons every second. (Because of E=mc2 equation).
• The Sun will take 4 protons, and produce one helium atom (2 protons + 2 neutrons) with 2 positrons and also 2 neutrino and 25 MeV of energy.
• The Helium atom and the 2 positrons weight less that the initial 4 protons (so part of the initial mass is converted into energy in the process).
• A hundred trillion neutrinos are going through our body every second.
• In a supernovae, 99% of the energy is released as neutrinos.
• Our sun is probably a third generation star.
• Betelgeuse in the orion constallation weights about 20x the mass of our sun and it is about to explode soon…
• There is a ratio of 3:1 for Hydrogen / Helium produced at the big bang.
• Heavier elements than iron might have been created during supernovae (but this is not sure at all).
• The Higgs Boson was discovered lately in the Large Hadron Collider (LHC).
• To claim for an evidence we only require “$3\sigma$” of precision (eg. 99.7%).
• To claim for a discovery we require “$5\sigma$” of precision (eg. 99.99994%). (based on normal distribution)
• The kinetic energy of the quarks is what we are measuring as the mass of a proton.
• The electromagnetic force and the weak force are very similar: there was a symetry between them, but somehow, the symetry got lost (spontanous symetry breaking) and thus is not valid anymore in the current universe.
• The higgs boson froze in the universe at about 4 quadrillion degrees.
• public/courses/physics/from_big_bang_to_dark_energy/intro.txt