Astronomical Motion Basics terms and concepts Force: action that changes the state of motion of an object. Inertia: the resistance of an object to the change of its state of motion. "mass" has two meanings: amount of matter measure of inertia (more massive bodies are more inert)

Speed, Velocity and Acceleration Speed is a scalar quantity which refers to "how fast an object is moving." 50 mi/h Instantaneous speed: the speed in an instant Average speed = total distance covered / duration of travel Velocity is a vector quantity which refers to "how fast an object is moving and to where.“ 50 mi/h to the North Acceleration – how does the velocity change

The Second Law of Newton: a = F/m, or F = ma Force a m Acceleration: the rate of change of velocity - speeding up, slowing down, or changing direction of motion "The acceleration of an object is proportional to the net force on it and inversely proportional to its mass". The bigger the force, the bigger the acceleration. The bigger the mass the smaller the acceleration.

Swing mass tied to a string in a circle String exerts force on the mass Without the force – motion on a straight line

Universal Gravitational Force Every two masses, M and m, attract each other with a force proportional to them, and inversely proportional to the square of the distance between them: M m d G is the gravitational constant, measured experimentally, G=6.67x10-11 Nm2/kg2

Key Ideas Kepler’s Laws Newton’s Laws Law of Universal Gravitation P 2 = a3 Newton’s Laws Speed, velocity, acceleration, force, inertia, mass, balanced and unbalanced forces F= ma Law of Universal Gravitation

Kepler’s Laws reconsidered Newton’s version of the Kepler’s 3rd empirical law: M m a P Units: P - in seconds, a - in meters. Allows to calculate masses

Newton figured out that the gravitational attraction between two objects is given by: where F is the force of attraction, G is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them. If we increase the mass of the first object twice, the force will become a. 32 times weaker b. 8 times weaker c. 2 times stronger d. 8 times stronger e. none of the above is correct

Light Basics How does light travel? fast & straight: 300,000 km/s Macroscopic Properties of Light reflected refracted blocked absorbed and re-emitted Nature of Light electromagnetic wave particle (photon) About 186,000 miles per second [300,000 kilometers per second], so light from the sun takes about 8 minutes to go 93 million miles [149 million kilometers] to earth. Does this seem SLOW? Well, if you could DRIVE to the sun at 60 mph [100 kph], it would take you 177 years to get there! In one second, light can go around the earth 7 times! Perfectly straight, until something bends it. The straight paths of light are called LIGHT RAYS.

Properties of Waves Frequency = 1/Period : f = 1/T Wave pulse wave Frequency = 1/Period : f = 1/T f is measured in 1/sec, or Hz Velocity = wavelength x frequency: v = lf Velocity is measured in m/s Light wave in vacuum : c = 300 000 km/s = lf Huge range in l and f c = lf always!!! wavelength is the distance between individual waves (e.g. from one peak to another). The wavelengths of visible light range between 400 to 700 billionths of a meter. But the entire electromagnetic spectrum extends from one billionth of a meter (for gamma rays) to meters (for some radio waves). The frequency is the number of waves which pass a point in space each second. Visible light frequencies range between 430 trillion waves per second (red) and 750 trillion waves per second (violet). The entire electromagnetic spectrum has frequencies between less than 1 billion waves per second (radio) and greater than 3 billion billion waves per second (gamma rays). Light waves are waves of energy and the amount of energy in a wave is proportional to its frequency. Wavelength increases, while frequency and energy decreases as we go from gamma rays to radio waves. All electromagnetic radiation travels at the speed of light (186,000 miles or 300,000,000 meters per second in a vacuum). Objects in space send out electromagnetic radiation at all wavelengths - from gamma rays to radio waves. Each type of radiation (or light) brings us unique information so, to get a complete picture of the Universe, we need to study it in all of its light, using each part of the electromagnetic spectrum! Almost everything we know about the Universe comes from the study of the electromagnetic radiation emitted or reflected by objects in space. Amplitude

A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami? A) 0.933 Hz B) 0.000259 Hz C) 1.07 Hz D) 0.148 Hz Answer: B

Examples of Mechanical Waves Need a medium to propagate Water waves tuning fork: vibrating object can produce sound Waves in a Guitar String Pressure waves

Light is a special kind of wave Oscillating electric charges (for example, in antennas) => produce changing magnetic field            => which produces changing electric field => which produce changing magnetic field,   and so on… Propagates both in vacuum and materials Electric and Magnetic fields are coupled: one produces the other. This creates an Electro-Magnetic wave that travels in direction perpendicular to both fields.  See a demo here.

Fig.06.05 Types EM waves c = lf When we look at the world around us we are seeing visible light waves (or visible radiation). However, there are many other forms of radiation that we cannot see with our eyes. These types include gamma rays, x-rays, ultraviolet, infrared, microwaves and radio waves. Together with visible light, all these types of radiation make up what we call the electromagnetic spectrum - the complete spectrum of radiation. Light (or radiation) is made up of vibrating waves of electrical and magnetic fields. This is where the term electromagnetic radiation comes from. Electromagnetic radiation travels in waves which have different wavelengths, energies and frequencies.

White Light Made up of all wavelengths

Energy Levels for the Hydrogen atom and possible emission lines Fig. 16.9 Energy Levels for the Hydrogen atom and possible emission lines Each element, isotope of that element, and even ionization level of that isotope has a different set of allowed orbits, and therefore emits and absorbs a different set of spectral lines. Small change in energy – redder color Spectrum Radiation of different wavelength and frequency is obtained

The “Fingerprint” of Different Elements Each element has its own family of unique spectral lines. Each element, isotope, and ionization level has a different energy shell structure. Each element, isotope of that element, and even ionization level of that isotope has a different set of allowed orbits, and therefore emits and absorbs a different set of spectral lines.

Three types of stellar spectra Spectra of stars 1. Lines 2. Background The spectrum of different objects is different depending on the state of that material. The three different cases include: A hot, dense material A “cool” gas (a diffuse gas in which the light primarily comes form a hot object beyond the gas. A “hot” gas, in which the light comes from the gas itself. In order to obtain and observe a continous spectrum – need source of large density 1. For a particular gas: wavelengths of absorption-lines identical to wavelengths of emission lines 2. Each chemical element has its own unique spectrum 3. Same cloud of gas can produce emission or absorption spectrum

Different stars – different spectra Can be organized into groups – not that many 300 000 stars –into 10 grouprs

Fig. 7.6 1. Wien’s law 2. Stefan – Boltzmann law T (heat) ~ random motion of particles

Doppler Effect λ ~ 550 nm λ ~ 600 nm Source of light receding from us at high speed

Doppler Effect Christian Johann Doppler (1803-1853) Information about the motion of the object Calculating the Doppler Shift Normal wavelength Source approaching the observer: waves bunched up ahead of it – λ decreases Source receding from the observer: waves are stretched out – λ increases

Refraction Reflection

Law of Reflection

The optical effect of refraction Speed of light different in different materials Vacuum – c =300 000 km/s Material – v < c Less dense to more dense – bands toward the normal line Index of refraction c/v = n >1 Bending Light If you have ever half submerged a straight stick into water, you have probably noticed that the stick appears bent at the point it enters the water (see Figure 1.) This optical effect is due to refraction. As light passes from one transparent medium to another, it changes speed, and bends. How much this happens depends on the refractive index of the mediums and the angle between the light ray and the line perpendicular (normal) to the surface separating the two mediums (medium/medium interface) (See Figures 2a and 2b.) Each medium has a different refractive index (see list below.) The angle between the light ray and the normal as it leaves a medium is called the angle of incidence. The angle between the light ray and the normal as it enters a medium is called the angle of refraction. Snell's Law In 1621, a Dutch physicist named Willebrord Snell (1591-1626), derived the relationship between the different angles of light as it passes from one transperent medium to another. When light passes from one transparent medium to another, it bends according to Snell's law which states: Ni * Sin(Ai) = Nr * Sin(Ar), where: Ni is the refractive index of the medium the light is leaving, Ai is the incident angle between the light ray and the normal to the meduim to medium interface, Nr is the refractive index of the medium the light is entering, Ar is the refractive angle between the light ray and the normal to the meduim to medium interface.

Optical Telescopes: Near Infrared and Visible Astronomy Mirrors are better: Lenses don’t produce clear image Lenses absorb some light Lenses are heavier Lenses change shape with time reflectors (with mirrors) refractors (with lenses)

What is important for a telescope? Diameter of the objective mirror (lens) Light-gathering power Angular resolution (in arcsec): The Focal Lengths Magnification

Yerkes Observatory

Atmospheric Absorption

Atmospheric Absorption

Astronomy at radio-wavelengths Earth’s atmosphere largely transparent Can penetrate dusty regions of interstellar space Observations in daytime as well as at night High resolution requires large telescopes Surface of planets (Venus) Planetary magnetic fields Structure of Milky Way and other galaxies Cosmic Background Radiation

The 64 meter radio telescope at Parkes Observatory, Australia A radio telescope is a form of radio receiver used in astronomy. In contrast to an "ordinary" telescope, which receives visible light, a radio telescope "sees" radio waves emitted by radio sources, typically by means of a large parabolic ("dish") antenna, or arrays of them. The 64 meter radio telescope at Parkes Observatory, Australia

Fig.06.40 Arecibo Observatory, Puerto Rico Constructed in natural limestone bedrock

The very large array (VLA) Central New Mexico 27 independent radio dishes, 25m each, spread over large distance Better resolution

Near Infrared and Visible Astronomy Earth’s atmosphere transparent to visible light, but only partly to IR light Near IR can penetrate dusty regions of interstellar space Surface of planets Physical Properties of Stars Structure of Milky Way, other galaxies and the Universe Other Solar Systems Searching for the first stars and galaxies

One of the two Keck telescopes Existing Large Optical Telescopes 1.5-m Mt Wilson 2.5-m Mt Wilson 5.0-m Mt Palomar 6.5-m Russia 10-m Keck, Mauna Kea, Hawaii 8.2-m VLT, ESO, Chile Many 3 – 3.5 m telescopes Several 6-6.5 m telescopes One of the two Keck telescopes

Fig.06.26

Fig.06.35

'Super Earth' Discovered at Nearby Star Exploring Other Solar Systems Very difficult to see small planets Need superb resolution A lot of planet hunting has been done during the last 5 years. To discover planets around stars 50 lyrs away, one needs state-of the art equipment and advanced knowledge in image processing in order to distinguish the Most of the more than 120 planets found beyond our solar system are gaseous worlds as big or larger than Jupiter, mostly in tight orbits that would not permit a rocky planet to survive. 25 August 2004 In a discovery that has left one expert stunned, European astronomers have found one of the smallest planets known outside our solar system, a world about 14 times the mass of our own around a star much like the Sun. It could be a rocky planet with a thin atmosphere, a sort of "super Earth," the researchers said today. Still, the discovery is a significant advance in technology: No planet so small has ever been detected around a normal star. And the finding reveals a solar system more similar to our own than anything found so far. Terrestrial in nature The star is like our Sun and just 50 light-years away. A light-year is the distance light travels in a year, about 6 trillion miles (10 trillion kilometers). Most of the known extrasolar planets are hundreds or thousands of light-years distant. The discovery was made with a European Southern Observatory telescope at La Silla, Chile, working at the verge of what's possible to detect. 200 giant planets 1 rocky planet 'Super Earth' Discovered at Nearby Star

“OverWhelmingly Large telescope” The most ambitious project from ground is the OWL ~ 25 Earths At the visual range we will be able to distinguish between 2 stars 0.001 arcsec apart

Ultraviolet, X-ray, Gamma-ray and Far IR Astronomy Observations must be made from space UV and X-ray: special mirror configurations needed to form images Gamma-rays cannot form images Stellar structure and evolution Structure of Milky Way and other galaxies

Fig.06.34 Mauna Kea Observatory, Hawaii

Fig.06.33 Cerro Tololo Inter-American Observatory

Basic Properties of Stars Talking about our galaxy and other galaxies we have to talk how do we measure distances in astronomy

Stellar parallax The apparent change in the position of a star caused by the motion of the Earth around the Sun is called parallactic shift. The parallactic shift is the largest, when obtained from two positions of the Earth’s orbit 6 months appart, as in Figure 1. The annual (or heliocentric) parallax is half the maximum parallactic shift. 1. Apparent change in the position of a star caused by the motion of the Earth around the Sun. 2. Detecting parallaxes means that Earth orbits around Sun 3. Maximum parallactic shift (two positions of the Earth’s orbit 6 months apart)

Proxima Centauri: distance : 4.3 LY = 4.3/3.26 pc = 1.3 pc Earth in December 1 2 3 A Figure 2 B b d November July A simple relationship (often called parallax-distance formula) between distance in parsecs and stellar parallax in arcseconds Proxima Centauri: distance : 4.3 LY = 4.3/3.26 pc = 1.3 pc parallax : 0.76 arcsec

Luminosity depends on temperature and size Luminosity ~ T4R2 Measure of true stellar brightness Luminosity the total amount of energy a star radiates out into space each second Tells us how much energy is being generated within the star Amount of generated energy is different for different stellar types !!! Same distance to both !!! !!! Same distance to both !!!

Apparent brightness Real Sky: Stars of different size and color (different luminosity) Different distances Energy reaching us depends on distance, T, R Apparent brightness - the true brightness affected by distance Far away Need to know stellar distances! Nearby

The brightness of the source of light decrease as we recede from it. Imagine an observer located at a distance d from a 150 Watt light bulb. Let’s call the brightness of this bulb, as seen by this observer, B. When the observer recedes from the bulb, the brightness B drops off as the square of the distance d. The brightness B and the distance d are related as Inverse-square dependence

Apparent brightness, true brightness, distance, magnitude scale 6 groups of visible star brightest - 1st magnitude faintest - 6th magnitude Apparent brightness and apparent mag m An increase of 1 mag corresponds to a decrease in brightness by a factor of ~2.5 times An increase of 5 mag corresponds to a decrease in brightness of 100 times True brightness All stars artificially moved at distance from Earth 10 pc: Intrinsic brightness (luminosity) and absolute mag M m -M = 5 log (d / 10)