Hubble's Law
Cosmic history Age in billions of years 0 Big bang. The universe is a plasma. .0003 The universe cools until the plasma becomes neutral matter. The universe is a cold dark gas. .15 Gravity collapses the gas and stars and galaxies begin forming. 1 Galaxies have formed, including the Milky Way. 9 Sun and Earth formed. 13 ~ 600 million years ago, oxygen became abundant in the Earth's atmosphere and multicellular life emerged. The tetrapod design emerged ~ 525 million years ago. 13.7 Present 18 The Milky Way and Andromeda collide. 19 Sun becomes a red giant and consumes the Earth. >20 The galaxies in the Local Group merge into one supergalaxy. Dark energy overwhelmes gravity and causes a runaway expansion of the universe and drives away all galaxies that haven't already merged with the Milky Way. 1000 The last stars burn out. The universe is dark hereafter.
Hubble's Law If a galaxy is sufficiently distant (beyond 100 million light years), then its speed with respect to the Milky Way is Speed = Hubble_Constant * Distance where the velocity is directed away from us. Hubble_Constant = 23 km/s/megalightyear Distance (million Mass Speed with respect Speed from Hubble light years) (Solar masses) to Milky Way (km/s) law (km/s) Edge of universe 13700 300000 300000 Coma Cluster 321 7*10^14 6950 7400 Virgo Cluster 54 1.2*10^15 1250 1240 Andromeda 2.54 3*10^12 -120 58 Milky Way .0248 3*10^12 Andromeda is near enough for gravity to have changed its velocity from the Hubble velocity. The Virgo Cluster is too far. Mass of sun = 2.0e30 kg Age of universe = 13.7 billion years Speed of light = 3.0e8 m/s
Escape velocity M = Mass of object R = Distance from object G = Gravitational constant = 6.67*10^-11 m^3 / kg / seconds^2 m = Mass of object trying to escape V = Escape velocity Gravitational potential energy = Kinetic energy G M m / R = 1/2 m V^2 V = (2 G M / R)^.5 What is the escape velocity of the Milky Way with respect to Andromeda and the Virgo cluster? If Andromeda and the Milky are initially at rest at their present distance, how long would it take for gravity to bring them together? How about the Virgo cluster and the Milky Way? To estimate this, assume a constant acceleration equal to the acceleration when they are at their initial distance. Given that the Hubble constant is equal to 23 km/s/megalightyear, estimate the age of the universe. Assume that the universe has been expanding at a constant rate since the big bang. Suppose you are near a 1 solar mass blackhole and your feet are 2 meters closer to the hole than your head. How close do you have to be to the hole for the difference in acceleration between your head and feet to be 100 m/s^2? The event horizon radius of a 1 solar mass black hole is 3.0 km.