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Why do the stars shine?
Lecture 8
CAPSTONE 07/14/2011
CPSTNE.Sunshine 07.14.2011
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
CPSTNE.Sunshine 07.14.2011
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?
CPSTNE.Sunshine 07.14.2011
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 (4R3/3)
• Erad (total)=(GM/2R)(mHnH4R3/3)=GM2/2R.
CPSTNE.Sunshine 07.14.2011
• 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.
CPSTNE.Sunshine 07.14.2011
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
• (origin of Agent 007, who is always stopping bombs
from going off)
CPSTNE.Sunshine 07.14.2011
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
• 20 times the apparent age of Earth!
• So, nuclear reactions could explain the above
CPSTNE.Sunshine 07.14.2011
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
CPSTNE.Sunshine 07.14.2011