Homework 1

Due 31Jan 2002

R&D: 16-17, 17-11, 18-1, 18-2, 18-12, 18-13

Problems: 16-8, 16-13, 17-9, 17-14, 18-1, 18-10

Current Event (astronomical article) write-up

Solar Neighborhood

Fig. 17.2

Luminosity of the Sun

Peak of the Electromagnetic Spectrum occurs at 5780 K

Wien's Law: lµconstant/T⁴

F= sT⁴ (Stefan's Law)

F = Energy/area/s

Luminosity=F · area

Fig. 3.11

Solar Spectrum

What can we learn from Spectrum and lines?

Temperature

Density

Composition

Fig. 16.8

Spectral Classes

Why are hydrogen absorption lines strongest in A type stars?

Proton-proton Chain

Proton-proton chain

Where is the Energy?

Proton-proton chain: essentially 4 protons become helium-4

Energy is released in gamma ray radiation

Net reaction is: 4(¹ H) ⁴ He + energy + 2 neutrinos

Energy comes from the difference in the mass of 4 protons and helium-4

Mass is energy energy is mass

Energy is Mass

Net reaction is: 4(¹ H) ⁴ He + energy + 2 neutrinos

Mass of 4 protons = M (4p) = 4( mass of a proton)

= 4(1.672630x10^-27 kg) = 6.6943x10^-27 kg

Mass of ⁴ He = 6.6466x10^-27 kg

M (4p)-M (⁴ He) = 0.048x10^-27 kg

E = mc² = 0.048x10^-27 kg (3x10⁸ m/s)² = 4.3x10^-12 J

J=kg m/s²

1kg 6.4x10¹⁴ J

Brightness vs. Luminosity

Brightness is

What we measure on Earth

Distance dependent

Apparent

Luminosity

Intrinsic property

Distance independent

Absolute

Absolute Magnitude

m_sun= -26.8

M_sun= 4.85

Absolute magnitude, M, is the apparent magnitude of an object measured at a distance of 10 pc.

In Fig. 17.6 Star B is brighter, but more distant. An observer sees Star A and B appearing to have the same brightness

Spectroscopic Parallax

A star's spectrum uniquely identifies the type of star

From the type of star, which tells you the approximate size, and brightness, one can find the distance

H-R Diagram

Nearby stars on left, Bright stars on right

Masses of Nearby Stars

Distribution of masses of main sequence stars in the solar neighborhood

Fig. 17.23

H-R Diagrams

Draw several H-R diagrams:

Increasing luminosity

Increasing mass

Longer lifetime for main sequence stars

Increasing radius

Stellar Radii

The larger the radius, the more surface area, the larger the luminosity

L µ T⁴ R²

Mass

Mass increases upward on the H-R diagram

Stellar Properties

Measuring radius, luminosity, and temperature

Determination of Mass: Visual

Binary systems:

Visual

Spectroscopic

Eclipsing

Kepler's laws to get Mass

Visual binary on right

Fig. 17-19

Determination of Mass: Spectroscopic

Motion caused by orbit about center of mass in system produces Doppler shift that can be measured

Accurate within 25%

Fig. 17-20

Determination of Mass: Eclipsing

Light intensity changes due to blockage by one star in front of the other

Fig. 17-21

Stellar Lifetimes

Stellar radii and luminosity vs. Mass. Fig. 17.24

The more luminous or massive a star is, the shorter the lifetime

Extending the Distance Scale

Fig. 17-17