Exam 2: Ch. 3, 5, and 6 Flashcards
Tycho Brahe
- most accurate pre-telescope observations
- his data showed that the positions of the planets deviated from those predicted by Ptolemy’s model
Johannes Kepler
- Brahe’s assistant
- tasked with analyzing the data to find a satisfactory model of the motion of the planets
- Kepler did not have full access to Brahe’s data until after Brahe died, and then he was eventually able to unravel the principles governing the motion of the planets
orbit
- path of an object through space
- can be open or closed
ellipse
all the points for which the sum of the distances between two points is always the same: the two points are the foci (one is a focus)
major axis
the longest diameter of an ellipse
semimajor axis
half of the major exis
eccentricity (e)
- a measurement of its “flatness”
- relationship of the distance between the foci and the length of the major axis
- the two extremes are e = 0, which is a circle; and e = 1, which is just a line
foci
the two points along the diameter of an ellipse
easy way to find a planet’s average distance to its sun?
the length of the semimajor axis
Kepler’s 1st Law
Each planet moves around the Sun in an orbit that is an ellipse with the Sun at one focus of the ellipse
do planets change speed throughout their orbit?
yes, the planet moves faster when it is closer to the Sun and slower when it is farther from the Sun
Kepler’s 2nd Law
The straight line joining a planet and its Sun sweeps out equal areas in space for equal intervals of time
Kepler’s 3rd law
- The square of a planet’s orbital period equals the cube of the semimajor axis of its orbit
- P^2 = A^3
- period of Mars is 1.88 years
- What is Mar’s semi-major axis?
(1.88^2)⅓ = 1.52 AU
- semimajor axis of Saturn is 9.54 AU
- What is Saturn’s period?
(9.54^3)½ = 29.47 years
Newton’s 1st law
- every object will continue to be at rest or move at a constant speed in a straight line unless it is acted on by an outside force
- “law of inertia”
- Without an outside force, the motion of an object doesn’t change
momentum =
mass x velocity
speed =
change in location / time
velocity =
directional speed of an object
Newton’s 2nd law
- the change in motion of an object is proportional to and in the direction of a force acting on it
- F = m x a
acceleration =
changes in velocity
Newton’s 3rd law
- for every action, there is an equal and opposite reaction
- Interactions between objects
- Object 1 exerts force on object 2, the 2 exerts force on 1 in opposite direction
Conservation of momentum
Total momentum of the collection of objects remains the same over time
mass
measurement of the amount of matter in an object
volume
the amount of space an object takes up
density =
mass / volume
Angular momentum
- a measure of rotation of an object around a reference point
- Product of mass, velocity, and distance from a reference point
Newton’s universal law of gravitation
Fg = G x M1 x M2 / R^2
M1M2: masses of two objects
R: distance between their centers
G: gravitational constant, G = 6.67 x 10-11
gravity and distance relationship
follows an inverse square law
what determines acceleration due to gravity
the central object
weight
the gravitational force on an object
perihelion
part of orbit closest to Sun
aphelion
part of orbit farthest from Sun
perigee
the part of a moon/satellite’s orbit that is closest to Earth
apogee
a moon/satellite’s farthest point in its orbit from Earth
satellite
any object that orbits another object
how far off the ecliptic do all the planets orbit the sun
within ~10* of the ecliptic
what are the only planets without moons
mercury and venus
where is the asteroid belt
between mars and jupiter (2.2 - 2.3 AU)
Low earth orbit
Example is ISS
Altitude of 400 km
Orbital speed of 8 km/s
Orbital period of ≈ 90 minutes
what is the escape speed of earth
~11 km/s
how fast do waves move?
speed of light
wavelength(λ)
the distance from crest to crest
frequency(f)
- the number of waves that passes a given point in a given time
- Measured in Hz
period
the time for one wavelength to pass
photon
EM light waves acting like a particle
propogation of light
- waves spread out in all directions from the source
- As the wave gets farther from the source, energy gets spread out more and more
relationship between the intensity of light and distance
- intensity decreases as the distance squared
- inverse square law
EM spectrum
the entire distribution of electromagnetic radiation according to frequency or wavelength
EM spectrum highest to lowest frequency
Gamma rays, x-rays, ultraviolet, visible, infrared, microwaves, radio waves
what waves reach earth’s surface
Only visible light, radio waves, and some UV and IR reach the surface of the earth
absolute zero
defines 0K as the lowest possible temperature
0K =
≈ -273*C
blackbody
an object that absorbs all radiation hitting it; as it heats up, it radiates until it reaches equilibrium
Wien’s law
λ where emission peaks get shorter as the temp rises
λmax =
Stefan-Boltzman law
power emitted per area
F(energy flux)
absolute luminosity
the power of a star
L =
reflecting
light bouncing off a surface at the same angle they arrive
refracting
- light bends as it moves through material
- the higher the frequency, the more the light bends
dispersion
occurs when light of multiple wavelengths gets refracted, the wavelengths separate
spectrometer
any device that separates light into different wavelengths
stellar spectrum
- what we get when we send a star’s light through a spectrometer
- In the Sun’s spectrum, we see the rainbow with some colors “missing”, showing up as dark lines
what happens when you send white light through a transparent gas
you get the same result as a continuous rainbow with dark lines
continuous spectrum
“full rainbow”, all the colors/wavelengths
absorption spectrum
continuous spectrum with dark lines(missing wavelengths)
emission spectrum
a spectrum of the electromagnetic radiation (different wavelengths) emitted by a source
how can we determine the makeup of a star?
Once we know a specific gas’s spectral fingerprint, we can look for it in the spectrum of a star
the makeup of an atom
- All atoms consist of positively charged protons, negatively charged electrons, and uncharged neutrons
- Protons and neutrons reside in a tightly packed nucleus in the center of an atom
- Electrons reside around the nucleus
atomic number
element is determined by the # of protons
neutral atoms
always have the same number of protons and electrons
ion
If #s of protons and electron are unequal, the atom has a non-zero charge
isotope
an atom of an element with different #s of protons and neutrons
atomic mass number
the # of protons + # of neutrons
Bohr model
Electrons can only be at certain distances/levels from the nucleus, and at each of these distances/levels, the electron’s energy is constant
Orbits(energy levels/states)
electron distances from the nucleus
what happens when electrons go to a higher/lower state
That energy goes in/out as a photon
h
Plank’s constant
Lyman series
transitions to/from the ground state (n = 1), emission/absorption of UV light
Balmer series
transitions to/from the first excited state (n = 2), emission/absorption of visible light
Paschen series
transitions to/from the second excited state (n = 3), emission/absorption of IR light
Bracket series
transitions to/from the third excited state (n = 4), emission/absorption of far IR light
Pfund series
transitions to/from the fourth excited state (n = 5)
Humphreys series
transitions to/from the fifth excited state (n = 6)
what was the first series observed?
the Balmer series were the first lines observed (because four of them are in the visible range), and they are often called “H-alpha,” “H-beta,” “H-gamma,” and “H-delta”
what is a way that electrons can get up to higher energy levels without a light source?
through collisions with other atoms, because temperature is a measure of atomic motion
ionization
- if enough energy is absorbed by an electron, it can escape its atom completely
- atoms can also recapture electrons, giving off one or more photons
how can you tell if the source of waves is moving toward an observer?
the waves pile up
how can you tell if the source of waves is moving away from an observer?
the waves become farther apart
doppler effect
if the source of waves is moving toward an observer, the waves pile up closer together; if the source is moving away, the waves become farther apart
blueshift
if a light source is moving toward you, the light becomes more blue
redshift
if a light source is moving away from you, the light becomes more red
what does the radial speed of a star need to be to look noticebly redder or bluer?
10,000 km/s
telescope
gathers light
instrument
separates λ’s
aperature
the diameter of the opening that allows light into the telescope
how much more light do you collect if you double the diameter?
4x
focus of the lens
if all the incoming light rays are parallel, and the curved surfaces of the convex lens are shaped correctly, then all the light rays are refracted to this point
focal length
distance from the lens to the focus
eyepiece
to actually see the astronomical object, we then view the image through another lens
downsides to refracting telescopes
- the glass has to be perfect all the way through, and both curved surfaces must be perfectly shaped
- chromatic aberration
- the lens can only be supported at its edges, which places an upper limit on the size of the lens: if the lens gets too big, gravity will cause it to sag and distort the image
chromatic aberration
when light is refracted, dispersion occurs; in the context of lenses, this means that different colors are focused at different locations
primary mirror
design is concave and usually coated with something highly reflective, like silver, aluminum, gold
problems solved by reflecting telescopes
- only the reflecting surface needs to be perfect because light doesn’t go through
- reflection does not result in dispersion, so there is no chromatic aberration
- a mirror can be supported from below, so it can be much bigger than the lenses in refractors
prime focus
where the curved primary mirror focuses the light, which is above it in the tube of the telescope
secondary mirror
a flat mirror that redirects the light away from the prime focus to a viewing location
Newtonian focus
this design redirects the light sideways to exit the side of the telescope
Cassegrain focus
this design reflects the light back directly down to exit the telescope through a hole in the middle of the primary mirror
active control
modern computers correcting/avoiding sagging in real-time
Gemini active control
measures the sagging multiple times a second and exert forces on the back of the mirror to correct it
Keck active control
using many mirrors to act as one large mirror
what atmospheric obstacles prevent good telescope pictures?
weather, water vapor, light pollution, and bad seeing
how does weather obstruct telescopes?
clouds block light, precipitation could damage the telescope
how can water vapor obstruct telescopes?
absorbs light (mainly IR) before it reaches the surface
light pollution
extra light washes out the faint objects
bad seeing
- how unsteady the light is due to turbulent air
- causes twisting and bending of light, resulting in blurry images as well as why stars twinkle
resolution
- refers to how sharp images are, the smallest distinguishable features
- the smallest angle we can resolve
how is resolution measured
- in angle on the sky: recall that there are 60 arcminutes in a degree and 60 arcseconds in an arcminute, so one arcsecond is 1/3600 of one degree
- one arcsecond is the apparent size of a quarter at a distance of 5 km
adaptive optics
- a computer system measures the atmospheric distortion and controls a flexible mirror to undo the distortion
- brings the angular resolution down to 0.1 arcseconds or better in IR light
integration time
how long the detector is open/observing
charge-coupled device (CCD)
the detector that sorts visible light
Infrared observation challenges
- shortest IR wavelength (~10-6 m) is right around the largest wavelength a CCD can measure
- much of IR radiation is blocked by the atmosphere
- Most everyday objects emit IR radiation
- IR detectors must be heavily shielded
spectroscopy
investigation and measurement of spectra
radio
encodes sound into waves in the radio part of the spectrum
radio telescope
- consists of a concave reflector made of metal and a detector at the focus of the reflector
- Detects all radio wavelengths at once
- Radio telescopes can be located pretty much anywhere and can observe during the day
Interferometry
- combine the light collected by more than one telescope
- The longer the wavelength, the worse the resolution (for a given size dish)
interferometer array
- We can get better resolution if we link multiple radio telescopes together
- Resolution of the interferometer depends on the baseline (separation of telescopes) not the size of the telescopes
radar
a technique for measuring distance in which you send radiowaves at an object and time how long it rakes for the waves to bounce back
what waves don’t reach the earth’s surface?
Earth’s atmosphere blocks all gamma rays, x-rays, microwaves, and most UV, so to view those bands, we must put telescopes above the atmosphere
the largest airborne IR telescope
Stratospheric Observatory for Infrared Astronomy (SOFIA)
major space-based IR telescopes
- IR Astronomical Satellite (IRAS)
- Spitzer Space Telescope
Hubble Space Telescope (HST)
2.4-m telescope designed for visible-light observations (and a little IR and UV sensitivity, too)
Hubble Ultra-Deep Field (HUDF)
a 2.4-arcminute square image with a total exposure of nearly 100 hours; it contains over 10,000 galaxies, many of which formed very soon after the Big Bang
what wave observations must be done in space?
UV, x-ray, and gamma-ray observations must be done in space
grazing incidence
where x-rays come in and hit the mirror nearly parallel to the mirror so that they actually reflect
how can we “observe” gamma rays from the earth’s surface
- by measuring their interaction with the atmosphere
- Gamma rays excite charged particles in the atmosphere, which then emit their own radiation, which excites other particles and causes them to emit radiation
