Astronomical Motion Basics terms and Basics terms and

conceptsconcepts

the resistance of an object to the change of its state of motion.

action that changes the state of motion of an object.

"mass" has two meanings:

• amount of matter• measure of inertia (more massive bodies are more inert)

Force:

Inertia:

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:The Second Law of Newton: a = F/m, or F = maa = F/m, or F = ma

"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.

Acceleration: the rate of change of velocity - speeding up, slowing down, or changing direction of motion

m

Force a

Swing mass tied to a string in a circleString exerts force on the massWithout the force – motion on a straight line

Universal Gravitational Universal Gravitational ForceForce

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:

2d

MmGF

G is the gravitational constant, measured experimentally,

G=6.67x10-11 Nm2/kg2

M

m

d

•Kepler’s Laws

•P 2 = a3

•Newton’s Laws• Speed, velocity, acceleration, force, inertia, mass, balanced and unbalanced forces

• F= ma

•Law of Universal Gravitation

2d

MmGF

Key Ideas

Kepler’s Laws reconsideredKepler’s Laws reconsidered

Newton’s version of the Kepler’s 3rd empirical law:

Units: P - in seconds, a - in meters.

)(

4 322

MmG

aP

Allows to calculate masses

a

Mm

P

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

F Gm

1m

2

r2

Light Basics

How does light travel? fast & straight: 300,000 km/s

Macroscopic Properties of Light reflected refractedblocked absorbed and re-emitted

Nature of Light electromagnetic wave

particle (photon)

Properties of WavesProperties of Waves

Amplitude

Frequency = 1/Period : f = 1/T f is measured in 1/sec, or Hz

Velocity = wavelength x frequency: v = f Velocity is measured in m/s

Light wave in vacuum : c = 300 000 km/s = f

Huge range in and f

c = f always!!!

Wave pulsewave

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

tuning fork: vibrating object can produce sound

Need a medium to propagate

Water waves

Waves in a Guitar StringPressure waves

Light is a special kind of waveLight 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…

Fig.06.05

c = f

Types EM waves

White Light

Made up of all wavelengths

Fig. 16.9

Energy Levels for Energy Levels for the Hydrogen the Hydrogen atom and possible atom and possible emission lines emission 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.

Three types of stellar spectra

1. For a particular gas: wavelengths of absorption-lines identical to wavelengths of emission lines2. Each chemical element has its own unique spectrum3. Same cloud of gas can produce emission or absorption spectrum

Spectra of stars1. Lines2. Background

Different stars – different spectra

Fig. 7.6 1. Wien’s law

2. Stefan – Boltzmann law

)(

0029.0)(max KT

m

4TE

T (heat) ~ random motion of particles

Slide 21

Doppler Effect

Source of light receding from us at high speed

λ ~ 550 nm

λ ~ 600 nm

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

lightofspeedwavelengthreal

wavelengthrealwavelengthshiftedobjectofspeed

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

Optical Telescopes:Optical Telescopes:Near Infrared and Visible AstronomyNear Infrared and Visible Astronomy

reflectors (with mirrors)refractors (with lenses)

Mirrors are better: - Lenses don’t produce clear image- Lenses absorb some light- Lenses are heavier- Lenses change shape with time

•Diameter of the objective mirror (lens)

• Light-gathering power

•Angular resolution (in arcsec):

•The Focal Lengths

• Magnification

What is important for a telescope?What is important for a telescope?

diameter

wavelengthresolution 000,250~

2~ diameterpower

e

o

f

fm

Yerkes Observatory

Atmospheric Absorption

Atmospheric Absorption

• 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

Astronomy at radio-wavelengths Astronomy at radio-wavelengths

Surface of planets (Venus)Planetary magnetic fieldsStructure of Milky Way and other galaxiesCosmic Background Radiation

The 64 meter radio telescope at Parkes Observatory, Australia

Fig.06.40

Arecibo Observatory, Puerto RicoConstructed in natural limestone bedrock

The very large array (VLA)Central New Mexico27 independent radio dishes, 25m each, spread over large distanceBetter 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 twoKeck telescopes

Existing Large Optical Telescopes

1.5-m Mt Wilson2.5-m Mt Wilson5.0-m Mt Palomar6.5-m Russia10-m Keck, Mauna Kea,

Hawaii8.2-m VLT, ESO, Chile

Many 3 – 3.5 m telescopesSeveral 6-6.5 m telescopes

Fig.06.26

Fig.06.35

'Super Earth' Discovered at Nearby Star

200 giant planets 1 rocky planet

Exploring Other Solar Systems

Very difficult to see small planets

Need superb resolution

“OverWhelmingly Large telescope”

~ 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 evolutionStructure of Milky Way and other galaxies

Fig.06.34Mauna Kea Observatory, Hawaii

Fig.06.33Cerro Tololo Inter-American Observatory

Basic Properties of Stars

Stellar parallax

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)

Earth in December

1

2

3

A

Figure 2

B

b

dEarth in November

Earth in 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

sec

1

arcppcd

Luminosity depends on temperature and size Luminosity ~ T4R2

Measure of true stellar brightness

!!! Same distance to both !!!

!!! Same distance to both !!!

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

Apparent brightnessReal 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

NearbyNeed to know stellar distances!

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

24

150

dB

Inverse-square dependence

Apparent brightness, true brightness, distance, magnitude scale

• Apparent brightness– 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)