Today:

• Review

The idealized scientific method

• Based on proposing and testing hypotheses

• hypothesis = educated guess

© 2006 Pearson Education Inc, publishing as Addison-Wesley

What is a scientific theory?

• The word theory has a different meaning in science than in everyday life.

• In science, a theory is NOT the same as a hypothesis, rather:

• A scientific theory must:• Explain a wide variety of observations with a few simple

principles, AND• Must be supported by a large, compelling body of evidence.• Must NOT have failed any crucial test of its validity.

Unit conversions(it’s all about multiplying by 1)

The changing night sky

• The locations of stars, planets and the moon are not static. Why do they change?

• Due to two motions:– Rotation of Earth about axis (diurnal motion)

– Orbit of Earth around Sun (annual motion)

Seasons

Kepler’s laws

• 1) Planetary orbits are ellipses with the Sun at one focus.

• 2) Law of equal areas.

• 3) P2=a3

Newton’s laws

• 1) An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force.

• 2) The acceleration of an object is proportional to the net outside force acting on the object. (F=ma)

• 3) Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

The nature of light: Newton

The nature of light: Young

Frequency and wavelength

• wavelength: distance between two successive wave crests

• frequency: number of wave crests that pass a given point in one second

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υ =c

λυ = frequency of electromagnetic wave in Hz

c = speed of light = 3 ×108 m/s

λ = wavelength of light in meters

Blackbody radiation

The higher an object’s temperature, the more intensely the object emits electromagnetic

radiation, and the shorter the wavelength at which it emits most strongly.

blackbody: A perfect blackbody does not reflect any radiation; instead, it absorbs all radiation falling on it.

Blackbody radiation

Wien’s law

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λmax=0.0029 K m

Tλmax = wavelength of maximum emission in meters

T = temperature of object in K

Very useful for determining surface temperature of stars since you need to know only the dominant wavelength of the electromagnetic radiation from the star.

Stefan-Boltzmann law

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F =σT 4

F = energy flux in joules per square meter of

of surface per second

σ = constant, 5.67 ×10−8 W/m2 /K-4

T = objects temperature in K

• Joule = unit of energy, energy in 2 kg mass moving at 1 m/s

• Watt = unit of power, 1 W output means 1 J/s

• flux: rate of energy output per square meter of object

Energy of photon (wavelength)

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E =hc

λE = energy of photon

h = Planck’ s constant, 6.625 ×10−34 J s

c = speed of light

λ = wavelength of light

Spectroscopy

Spectrum of hydrogen: Bohr

Doppler shifts

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Δλλ0

=v

c

λ 0 = wavelength of stationary source

Δλ = wavelength shift ( Δλ = λ − λ 0)

v = velocity of source measured along line of sight

c = speed of light

Refracting telescopes

Reflecting telescopes

Limits to angular resolution

Diffraction is the tendency of light waves to spread out when they are confined to a small area (like a lens or mirror of a telescope). The beam in a telescope tends to spread out a bit which blurs the image.

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θ =2.5 ×105 λ

Dθ = diffraction - limited angular resolution of telescope in arcsec

λ = wavelength of light in meters

D = diameter of objective lens/mirror in meters

In practice, air turbulence makes the image jitter (the twinkling of stars) which makes even the diffraction limit unreachable on Earth. This is why we launch telescopes into space!