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Transcript

Why do the stars shine? Lecture 8 CAPSTONE 07/14/2011 07.14.2011 CPSTNE.Sunshine 07.14.2011 1 REVIEW Final distance comments (approximations) Sun is 1 AU from Earth, or 100 solar radii (Diameter of Sun = 1.39x 106 km.) Sun is 100 Earth diameters across (1.3 x 104 km) Edge of the Solar system is about 100 AU Distance of Oort Cloud is 100,000 AU Distance to nearest star is 200,000 AU (1 pc) Distance to center of the Galaxy is 8000 pc Distance to nearest big Galaxy is 800,000 pc Distance to nearest big Group is 5 Mpc. Distance to nearest cluster is 10 Mpc (Virgo) Distance to edge of the Universe is 30,000,000 Mpc 07.14.2011 CPSTNE.Sunshine 07.14.2011 2 3. Two galaxies orbit each other. Each has about 1011 solar masses, 1/5 in stars and 4/5 in dark matter. They are 100 kpc apart. What is the period? (7x109 years). How many orbits will they complete in the life of the Universe? 07.14.2011 CPSTNE.Sunshine 07.14.2011 3 Age of the Sun • Consider a cloud of mass M, full of hydrogen atoms, of radius R. Over time, each atom leads to a total radiation -U/2 for each atom (the mass interior to the radial distance of each particle is always acting as the total mass, M, at the center). • Total energy radiated is energy lost per particle times the no. of particles, which is particle density times volume. • Erad(total) =-Utot/2= (sum of individual U/2 for each atom)=(GMmH/2R) x nH x (4R3/3) • Erad (total)=(GM/2R)(mHnH4R3/3)=GM2/2R. 07.14.2011 CPSTNE.Sunshine 07.14.2011 4 • Note: R is now the radius of the star. The potential energy gain is U(initial)-U(final), but U(initial)=0 since the cloud radius is so much larger than the final star. • Assume the Sun has shown at constant luminosity for t years. Total energy radiated = L0x t=4x1033 ergs/sec x t. • (We know today that main sequence stars do not change luminosity over the life of mankind.) • Lt=GM2/2R, t=GM2/2RL • t = 15 million years • This is the ~Kelvin Helmholtz timescale and assumes that all the energy emitted by the Sun comes from gravitational energy (in the form of radiation). • But, the Sun has to be as old as the Earth, or 5 billion years. (radioactivity, Darwin). • There must be some other source of energy. 07.14.2011 CPSTNE.Sunshine 07.14.2011 5 Nuclear reactions • Note that the mass of He nucleus is less than the mass of 4 nucleons (2p, 2n) by 2.87% • Energy equivalent is 0.0287 x mH x c2 for each H. • = 4.288x10-5 ergs x 1/(1.6 x 10-12 erg/ev)=6.86 Mev/H • Or 28.72 Mev per He nucleus • 1 H atom is 109 ev, so =0.007 per H atom. • (28.72 x 106ev) / [(4 nucleons per He)x(109ev/nucleon)]=0.007 • (origin of Agent 007, who is always stopping bombs from going off) 07.14.2011 CPSTNE.Sunshine 07.14.2011 6 How much energy in the Sun? • • • • Total no. of H atoms x energy per atom? (M0/mH) x mHc2 x 0.007= 1.3 x 1052 ergs How long can the Sun shine? t=(1.3 x 1052 ergs)/4 x 1033 ergs/sec = 3.2 x 1018 sec x (1 yr./3.1 x 107 sec) • Or 1011 years (only ~10% of H needs to be burned) • 20 times the apparent age of Earth! • So, nuclear reactions could explain the above discrepancy. 07.14.2011 CPSTNE.Sunshine 07.14.2011 7 But, is there any proof it does? • Postulate nuclear reactions, ==>neutrinos should come from Sun. (very ephemeral) • 2002 Nobel Prize given to Ray Davis and Masatoshi Koshiba for detection. • Were found to be well below expected rate ( a problem for 25 years) • Led to discovery important in neutrino physics, but problem is resolved. • 60 years between postulate of nuclear energy and proof. (Recall parallax, age of Earth, etc. that all took time to get big dilemmas 07.14.2011 CPSTNE.Sunshine 07.14.2011 8 resolved)