Lecture 2

Examination The course is assessed in three parts: Problem sets. The problem sets and the peer reviews. One of the sets will randomly be corrected by me Observational labs. The laborative exercises + a lab report. Written Exam. It consists of two parts. Part I is needed for grade E: at least 75% needs to be correct. It is also needed to be able to go on to Part II, which is used to assess for grades A-D. The grade is set according to the score. To pass the course, all three of the above assessments must be ready. Objectives for grade E: For passing the course with grade E you need to know the fundamentals of the course. Objectives for grades A-D: Be able to solve problems on topics covered in the course, that need a well developped and mature understanding its content.

Pedagogical background for peer review: - See other solutions, comparing solutions. - The understanding gets deeper, when applying criteria for good/bad solutions; ”Is it really the correct solution for this problem? - Select good evidence to be able to convince others. - Learn to judge a good performance. You are included in the critique process. - All this leads to increased self-supervision capabilities. Other positive effects of this is that the feedback is prompt, and is relevant. In addition, learning from errors is very powerful. The possibility of erroneous thinking without the risk of being negatively judged by the teacher is important.

Repetition

Vernal equinox ”Vårdagsjämningspunkten” Right ascension Declination

The Sun appears to trace out a circular path called the ecliptic on the celestial sphere tilted at 23 ½ degrees to the equator The ecliptic and the celestial equator intersect at only two points Each point is called an equinox The point on the ecliptic farthest north of the celestial equator that marks the location of the Sun at the beginning of summer in the northern hemisphere is called the summer solstice At the beginning of the northern hemisphere’s winter the Sun is farthest south of the celestial equator at a point called the winter solstice June 21 March 31 Dec 21 Sept 21

Stellar Motions: Proper motion  r

Nature of Light - Cnt’d

Spectral Lines

Kirchhoff’s Laws

Bohr’s formula for hydrogen wavelengths 1/ = R x [ 1/N 2 – 1/n 2 ] N = number of inner orbit n = number of outer orbit R = Rydberg constant (1.097 X 10 7 m -1 ) = wavelength of emitted or absorbed photon Ly  Ly  HH HH

Balmer Lines in Star Spectrum

Photons’ interaction with matter: Extinction Absorption: Scattering: Interstellar grains and gas

Rayleigh scattering is responsible for the scattering of visible light in the daytime sky * Scattering on electrons * Proportional to 1/ 4 Scattering

Gravitation

Ancient astronomers invented geocentric models to explain planetary motions Like the Sun and Moon, the planets move on the celestial sphere with respect to the background of stars Most of the time a planet moves eastward in direct motion, in the same direction as the Sun and the Moon, but from time to time it moves westward in retrograde motion

A planet undergoes retrograde motion as seen from Earth when the Earth and the planet pass each other

Johannes Kepler proposed elliptical paths for the planets about the Sun Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion: 1.the orbits are ellipses 2.a planet’s speed varies as it moves around its elliptical orbit 3.the orbital period of a planet is related to the size of its orbit

Kepler’s First Law: A planet orbits the Sun in an ellipse, with the Sun at one focus of the ellipse Eccentricity Semiminor axis Focal point Semimajor axis Actually, the center-of-mass is at the focus

Kepler’s Second Law: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals Orbital speed depends on location

Angular momentum of a system is a constant for a central force law The time rate of change of the area swept out by a line connecting a planet to the focus of an ellipse is a constant = one-half of the orbital angular momentum per unit mass

Kepler’s Third Law (harmonic law): Relates the average orbital distance of a planet from the Sun to its period P 2 = a 3 P = planet’s sidereal period, in years a = planet’s semimajor axis, in AU

Kepler’s Third Law

Simple derivation using Newtonian mechanics gives that Kepler’s third law is

Galileo’s discoveries with a telescope strongly supported a heliocentric model The invention of the telescope led Galileo to new discoveries that supported a heliocentric model These included his observations of the phases of Venus and of the motions of four moons around Jupiter

One of Galileo’s most important discoveries with the telescope was that Venus exhibits phases like those of the Moon Galileo also noticed that the apparent size of Venus as seen through his telescope was related to the planet’s phase Venus appears small at gibbous phase and largest at crescent phase

Geocentric To explain why Venus is never seen very far from the Sun, the Ptolemaic model had to assume that the deferents of Venus and of the Sun move together in lockstep, with the epicycle of Venus centered on a straight line between the Earth and the Sun In this model, Venus was never on the opposite side of the Sun from the Earth, and so it could never have shown the gibbous phases that Galileo observed

In 1610 Galileo discovered four moons, now called the Galilean satellites, orbiting Jupiter

Isaac Newton formulated three laws that describe fundamental properties of physical reality Isaac Newton developed three principles, called the laws of motion, that apply to the motions of objects on Earth as well as in space These are 1.the law of inertia: a body remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force 2.F = m x a (the force on an object is directly proportional to its mass and acceleration) 3.the principle of action and reaction: whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body

Newton’s Law of Universal Gravitation F = gravitational force between two objects m 1 = mass of first object m 2 = mass of second object r = distance between objects G = universal constant of gravitation If the masses are measured in kilograms and the distance between them in meters, then the force is measured in newtons Laboratory experiments have yielded a value for G of G = 6.67 × 10–11 newton m 2 /kg 2

Kepler’s First Law: A planet orbits the Sun in an ellipse, with the Sun at one focus of the ellipse Eccentricity Semiminor axis Focal point Semimajor axis Actually, the center-of-mass is at the focus Elliptical orbits result from an attractive r -2 central force law such as gravity, when the total energy of the system is less than zero (a bound system). Parabolic path is obtained when E=0. Hyperbolic path in an unbound system E>0

Orbits may be any of a family of curves called conic sections

Orbits The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth Paths A, B, and C do not have enough horizontal velocity to escape Earth’s surface whereas Paths D, E, and F do. Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth

FIN

Tidal force

Gravitational forces between two objects produce tides

The Origin of Tidal Forces

Light has properties of both waves and particles Newton thought light was in the form of little packets of energy called photons and subsequent experiments with blackbody radiation indicate it has particle-like properties Young’s Double-Slit Experiment indicated light behaved as a wave Light has a dual personality; it behaves as a stream of particle like photons, but each photon has wavelike properties

Determining the Speed of Light Galileo tried unsuccessfully to determine the speed of light using an assistant with a lantern on a distant hilltop

Light travels through empty space at a speed of 300,000 km/s In 1676, Danish astronomer Olaus Rømer discovered that the exact time of eclipses of Jupiter’s moons depended on the distance of Jupiter to Earth This happens because it takes varying times for light to travel the varying distance between Earth and Jupiter Using d=rt with a known distance and a measured time gave the speed (rate) of the light

In 1850 Fizeau and Foucalt also experimented with light by bouncing it off a rotating mirror and measuring time The light returned to its source at a slightly different position because the mirror has moved during the time light was traveling d=rt again gave c

The number of protons in an atom’s nucleus is the atomic number for that particular element The same element may have different numbers of neutrons in its nucleus These three slightly different kinds of elements are called isotopes

Spectral lines are produced when an electron jumps from one energy level to another within an atom The nucleus of an atom is surrounded by electrons that occupy only certain orbits or energy levels When an electron jumps from one energy level to another, it emits or absorbs a photon of appropriate energy (and hence of a specific wavelength). The spectral lines of a particular element correspond to the various electron transitions between energy levels in atoms of that element. Bohr’s model of the atom correctly predicts the wavelengths of hydrogen’s spectral lines.

A planet’s synodic period is measured with respect to the Earth and the Sun (for example, from one opposition to the next)

Tycho Brahe’s astronomical observations disproved ancient ideas about the heavens

Parallax Shift

There is a correlation between the phases of Venus and the planet’s angular distance from the Sun

Newton’s description of gravity accounts for Kepler’s laws and explains the motions of the planets and other orbiting bodies

Each chemical element produces its own unique set of spectral lines

Bohr’s Model of the Hydrogen atom

Spectral line series of the hydrogen atom

Doppler Shifts Red Shift: The object is moving away from the observer Blue Shift: The object is moving towards the observer  = wavelength shift rest = wavelength if source is not moving v = velocity of source c = speed of light

The wavelength of a spectral line is affected by the relative motion between the source and the observer