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Unformatted text preview: The Main Sequence (Kutner, Ch. 9, Bennett et al. Ch. 14, and Shu Ch. 6) AST 203 (Spring 2011) Energy Sources (Canbll and Ostlie, Ch. 10) What provides the energy for a star?
Sun's lifetime must be consistent with observed fossil record.
19th century idea: contraction of the Sun Sun contracts —> becomes more tightly bound —> gravitational PE
released —> heat up, radiates energy away —> further contraction. AST 203 (Spring 2011) Gravitational Lifetime of a Star How long can gravitational contraction power the Sun? Recall the gravitational potential energy for two masses is Gmlmz
7" U:_ Spherical mass distribution, Newton proved: Outside spherical mass: force/PE is as if all the mass
concentrated at the center Inside a spherical mass: only mass inside your radius
contributes to force/PE. AST 203 (Spring 2011) Gravitational Lifetime of a Star spherical mass distribution: gravitational
potential energy of some point mass dm
located outside a mass M (r) is Take the point masses as a
spherical shells, then dm : 47rr2pdr AST 203 (Spring 2011) Gravitational Lifetime of a Star Gravitational potential energy: R
U = —47rG/ M(r)p7"dr
0 The result of this integral is something of the form
R Uz—a Where oz ~ 1 We could have also argued that this must be the form of the
gravitation potential energy just by dimensional analysis. Constant density result:
5 R U: AST 203 (Spring 2011) Gravitational Lifetime of a Star Gravitational potential energy for spherical mass: GM2 Uz—a R What does this mean? |U| is the energy that needs to be put into the system to
break it apart (move all the masses to infinity) |U| can also be thought of as the gravitational potential
energy that was liberated in assembling the spherical
mass We typically won't worry about the value of a—it is always
close to 1. AST 203 (Spring 2011) Gravitational Lifetime of a Star Timescale for gravitational potential energy to power the Sun: t : lUl
dE/dt What do we use as the energy rate, dE/dt ? We can use the luminosity of the present Sun. _ |U| N GM2/R — Q ~ Lo
7 6.67 X 10—8 dyn cm2 g‘2 (2 x 1033 g)2 /7 x 1010 cm
— 4 x 1033 erg s—1 t :9.5><1014s:3><107yr What's wrong with this number? AST 203 (Spring 2011) Gravitational Lifetime of a Star This timescale is called the Kelvin-Helmholtz timescale. Geological dating of moon rocks give age ~ 4 billion years—far
older than a gravitationally powered Sun can provide. Gravitational potential energy is ruled out. AST 203 (Spring 2011) Gravitational Lifetime of a Star Note: in the estimate we just did, we took It is important to note that this quantity is the amount of binding
energy since the Sun formed. Originally, the Sun was a cloud of gas in the Galaxy, and U ~ 0.
As the Sun formed and contracted, it reaches the present value
of U. AST 203 (Spring 2011) Chemical Lifetime of a Star Chemical reactions involve atomic processes (electrons)
Typical energy ~ 1 eV. How much chemical energy is there in the Sun? AST 203 (Spring 2011) Chemical Lifetime of a Star Sun is mostly hydrogen—number of atoms is N: M 2 ﬂ
mp 1.67 X 10—24 g Each atom contains ~1 eV of chemical energy—total energy: Ech : N - 1 eV 2 1.2 x 1057 eV 2 1.9 x 1045 erg
Chemical energy can power the Sun for Ed. 1.9 x 1045 erg 11
Ch LG 4 X 1035 erg 8—1 X S yr This is even less than the Kelvin-Helmholtz timescale! = 1.2 x 1057 AST 203 (Spring 2011) What's next? Even if chemical reactions provided 10 eV or 100 eV per atom—
still to short. Clearly, we need another energy source—nuclear energy. Before we can understand the yields from nuclear energy, we
need to learn some nuclear physics. AST 203 (Spring 2011) ...
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This note was uploaded on 05/04/2011 for the course AST 203 taught by Professor Simon,m during the Spring '08 term at SUNY Stony Brook.
- Spring '08