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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
• 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
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:
F G 2
G is the gravitational constant,
measured experimentally,
G=6.67x10-11 Nm2/kg2
Key Ideas
•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
F G 2
Kepler’s Laws reconsidered
Newton’s version of the Kepler’s 3rd empirical law:
4 a
P 
G(m  M )
Units: P - in seconds, a - in meters.
Allows to calculate masses
Newton figured out that the gravitational attraction between two
objects is given by:
F  G 12 2
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
absorbed and re-emitted
Nature of Light
electromagnetic wave
particle (photon)
Properties of Waves
 Frequency = 1/Period : f = 1/T
Wave pulse
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!!!
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…
Types EM waves
c = lf
White Light
Made up of all wavelengths
Fig. 16.9
Energy Levels for the
Hydrogen atom and
possible emission
Small change in energy – redder color
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
Spectra of stars
1. Lines
2. Background
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
Fig. 7.61. Wien’s law
lmax (m) 
T (K )
2. Stefan – Boltzmann law
E  T
T (heat) ~ random motion of particles
Doppler Effect
λ ~ 550 nm
Source of light
receding from us at high speed
Slide 21
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
shifted wavelength  real wavelength
speed of object 
 speed of light
real wavelength
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:
Near 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
What is important for a telescope?
•Diameter of the objective mirror (lens)
• Light-gathering power
power ~ diameter 2
•Angular resolution (in arcsec):
•The Focal Lengths
• Magnification
resolution ~ 250,000
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
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
•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
Existing Large Optical
Mt Wilson
Mt Wilson
Mt Palomar
Keck, Mauna Kea,
8.2-m VLT, ESO, Chile
Many 3 – 3.5 m telescopes
Several 6-6.5 m telescopes
One of the two
Keck telescopes
Exploring Other Solar Systems
Very difficult to
see small
Need superb
200 giant planets
1 rocky planet
'Super Earth' Discovered at Nearby Star
“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 evolution
Structure of Milky Way and other galaxies
Mauna Kea Observatory, Hawaii
Cerro 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
Figure 2
Earth in
Earth in
d  pc  
parc sec 
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
• 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
Far away
Need 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
B 
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)