During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. During the nineteenth century, scientists suggested that the Earth was hundreds of millions of years old. Today we know the Earth is 4.5 Billion years old. Today we know the Earth is 4.5 Billion years old. PROBLEM – HOW CAN THE SUN BURN SO HOT FOR SO LONG A TIME???? PROBLEM – HOW CAN THE SUN BURN SO HOT FOR SO LONG A TIME????

In the 1800’s Lord Kelvin and Hermann von Helmholtz suggested that as gravity collapsed the Sun, the gases would heat up. (Kelvin- Helmholtz contraction) In the 1800’s Lord Kelvin and Hermann von Helmholtz suggested that as gravity collapsed the Sun, the gases would heat up. (Kelvin- Helmholtz contraction) Kinda like a bicycle pump heats up compressed air. Kinda like a bicycle pump heats up compressed air. PE grav  Thermal Energy as star contracts PE grav  Thermal Energy as star contracts This process cannot be This process cannot be Calculations show that the sun would have had to start its contraction no more that 25 million years ago. Calculations show that the sun would have had to start its contraction no more that 25 million years ago. THE SOLAR SYSTEM IS MUCH, MUCH OLDER THE SOLAR SYSTEM IS MUCH, MUCH OLDER

A stars power output is called its LUMINOSITY. A stars power output is called its LUMINOSITY. What energy source produces this power??? What energy source produces this power???

Recall that Einstein predicted that there is an equivalence of mass and energy according to Recall that Einstein predicted that there is an equivalence of mass and energy according to E = mc 2 Consider the meaning of this. Consider the meaning of this. A small amount of mass can release a tremendous amount of energy A small amount of mass can release a tremendous amount of energy

Fusion Requires Extreme Conditions Fusion occurs during collisions Fusion occurs during collisions long range electrostatic forces work to keep positively charged nuclei apart long range electrostatic forces work to keep positively charged nuclei apart if nuclei come sufficiently close to one another, the stronger but shorter range nuclear forces work to pull nuclei together if nuclei come sufficiently close to one another, the stronger but shorter range nuclear forces work to pull nuclei together Fusion requires high temperatures: ~10 million K Fusion requires high temperatures: ~10 million K so that particles have the velocities or energies required to overcome electrostatic repulsion so that particles have the velocities or energies required to overcome electrostatic repulsion the higher the electrostatic force the harder a species is to fuse the higher the electrostatic force the harder a species is to fuse Fusion requires high densities Fusion requires high densities so that collisions are very common so that collisions are very common Particle Separation Repulsive Force Strong electrostatic repulsion at intermediate separation. Strong nuclear attraction at very small separation.

Figure from Foundations of Astronomy by M. Seeds

Each proton has a certain mass The resulting Hydrogen atom is less massive. Note that one of the protons converted into a neutron The mass defect is converte d into energy Positron – electron annihilation

Another proton can now combine with deuterium to form a low mass isotope of Helium A gamma ray is given off

Fusion and Mass Defect Consider this, Consider this, If 1kg of Hydrogen is converted into Helium, the helium will have a mass of 993 grams. The mass defect is converted to 6.3 x J of energy. (like burning 20,000,000 kg of coal)

Finally the Helium isotopes combine to produce Helium and 2 new protons

Consider the picture Consider the picture Recall Hydrostatic Pressure Recall Hydrostatic Pressure

Now consider a “slab” of solar material. Aka a layer of the Sun. Now consider a “slab” of solar material. Aka a layer of the Sun. The Suns interior is in hydrostatic equilibrium. The Suns interior is in hydrostatic equilibrium. In general there is a balance between In general there is a balance between Radiation pressure and Radiation pressure and Gravitational pressure Gravitational pressure

Each layer of a star is in thermal equilibrium. Otherwise the star would become too hot or too cold. ENERGY MUST BE TRANSPORTED TO THE SURFACE by radiative diffusion and convection

A diagram of the Sun

All stars have a certain Luminosity (L) Power output in Watts This information can tell us a lot about a stars history and current state. First we need to understand the inverse square nature of EM radiation.

d=1 d=2 d=3 B=1 B=1/9 B=1/4

How does the amount of paint caught by a 1 square unit area change with distance? How does the amount of paint caught by a 1 square unit area change with distance?

LUMINOSITY = THE AMOUNT OF ENERGY EMITTED IN 1 SECOND

IF YOU DIVIDE THE LUMINOSITY BY THE SURFACE AREA OF A SPHERE (where the detector would be)YOU GET...

(PSRT)

EXAMPLE PROBLEM A long time ago in a galaxy far far away Darth Vader is observing two different stars. Both stars are equally bright as observed from his location, but Star A is 10 pc away and star B is 20 pc away. Which star is more luminous? By how much?

Summary - Luminosity and Brightness Luminosity is an absolute value that measures the total power radiated by a star. Luminosity is measured in watts and tells us the rate that energy radiates from a star in all directions. Our Sun has a luminosity of about 3.90 x W. Luminosity is very important in providing information about star structure and age. Apparent brightness is a relative value. As observers on Earth, we perceive star brightness as the fraction of the luminosity received by us. We measure brightness in watts per square meter.

Luminosity and Apparent Brightness Apparent Brightness Apparent brightness is proportional to the luminosity of the star. Apparent brightness is inversely proportional to the square of the distance between the star and the observer. Apparent brightness depends on two variables:

Luminosity and Apparent Brightness This means that a brighter star is not necessarily closer to Earth, or larger, or hotter. A high luminosity star that is farther from Earth can still appear brighter.

Luminosity and Apparent Brightness When comparing two stars the same distance from Earth, the star with the greatest luminosity will appear brighter. Both the surface temperature and size of a star affect luminosity. These relationships are the topics of Wien’s and the Stefan-Boltzmann Laws

EXAMPLES Tsokos 5ed - # 1-3 pg. 504 Tsokos 5ed - # 1-3 pg. 504