Chapter 12 Flashcards
1 light year =
9.4 x 10^15m (or 10^16)
Key points about distance scale
- > Distances in the solar system can be measured by radar.
- > Distances to near by stars can we found by parallax
- > Some larger distances can be estimated by the apparent brightness of standard candles.
Our solar system contains…
Sun, Planets, Satellites, Asteroids and Comets
One way to measure distances in the solar system can be using
Radar
How does radar work?
A short pulse of radio waves is sent from a radio telescope towards a distant object, the pulse is then reflected back to earth. The telescope picks up this waves and records the time taken for it to return. As radio waves travel at the speed of light, c, you can work out the distance s= d/t
So the equation is…
2d = ct (2d because the pulse travels twice the distance to the object.)
You can also use this method to…
Find the speed of an object relative to the earth. You send two pulses separated by a certain time interval to give the measurement of it’s distance. The difference between the distances shows how far it has moved in the time interval.
This method is based on two assumptions…
- The speed of the radio waves is the same on the way to the object and the way back to the telescope
- The time taken for the radio waves to each the object is the same as the time taken to return.
For these assumptions to be true…
The speed of light must be constant
How bright a star looks from earth is called
Apparent magnitude (This depends on its absolute magnitude
So to find the distance of a star you need to…
measure how bright it looks (apparent magnitude) and calculate how bright it really is and put these into an equation.
You can calculate the brightness of objects directly using…
Standard candles
Cepheid variable stars are an example of…
Standard candles because their brightness changes in a certain pattern. So if you find a Cepheid variable within a galaxy, you can work out how far that galaxy is from us.
One astronomical unit is defined as…
The distance from the Earth to the Sun
Another distance of measure is the Light-Year, which is the…
Distance that electromagnetic waves travel through a vacuum in one year. So a star that is 10 light-years old, means we are actually seeing it 10 years ago.
One light year is equivalent to about…
63,000 Astronomical units
If you stand and listen to a car drive past you, the horn will sound lower if it is moving away from you and higher if it’s moving towards you, this is called the…
Doppler effect
Why does the car horn sound lower?
Because the sound waves are moving in the opposite direction from the car so have longer wavelengths and a lower frequency when they reach you.
The doppler effect means…
Radiation emitted by distant objects is “shifted”
How the radiation is shifted depends on its movement…
- When an object is moving away from Earth, the wavelengths of its radiation get longer and the frequencies get lower; it shifts towards the red end of the spectrum (redshift)
- When an object is moving towards Earth, the opposite happens to the radiation undergoes blueshift
The equation for the velocity of an object from the radiation it emits and absorbs is…
v/c = (change in wavelength)/ (wavelength of the emitted radiation)
-if v
Radiation is emitted from a very hot region of a star called…
photosphere in a continuous spectrum
Relativistic time dilation is…
a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses.
Recessional velocity
How fast the galaxy is moving away from earth
Hubble found that
the recessional velocity of galaxies against their distance from earth were proportional
Hubbles law…
v= H0d
Where v = recessional velocity in kms^-s
d= distance in Mpc ( Mpc = 3x 10^22)
H0= Hubbles constant in Kms^-1Mpc
The SI unit for H0 is…
s^-1
Because objects are moving away from each other this shows…
That Hubbles work is strong evidence the universe is expanding
Cosmological redshift…
Space itself is expanding and lightwaves are being stretched along with it
Redshifts of distant galaxies gives evidence of…
The expansion of the universe
Redshift equation
V/C = change in λ / λ
Current estimates of the expansion time scale of the universe is…
13.7 +- Gyr
The redshift of galaxies is strong evidence for the Hot BigBang
The universe started iff very hot and very dense and has been expanding ever since
Other evidence for the HBB
Cosmic Microwave Background radiation:
Models of the Big Bang show that, at the beginning of the universe, radiation of a relatively short wavelength would have been produced. Now, this radiation, due to the expansion of space, has been stretched - it has become microwave radiation.
Properties of cosmic microwave background radiation
- Corresponds to a temp of 2.73 k
- Radiation if largely isotropic and homogeneous
- Background radiation shows a doppler shift showing earths motion through space
More evidence for the HBB
- Large abundance of helium
- The early universe is very hot and it must’ve been hot enough for hydrogen fusion to happen and this produces helium
Hubbles law suggest thats…
The universe started with the big bang and has been expanding ever since
Current best estimate for the age of the universe…
1.5 x 10^10
speed of light
3 x 10^8 ms^-1
1 light-second
3 x 10^8 m
light-year
approx 10^16 m
Radar ranging and velocity of asteroid
-Send out the first radar pules, which then returns once it has collided with the asteroid.
-Then do the same after a certain time period.
-You can then work out the distance it travelled in between the two pulses using light-seconds
You can then use the time take in-between the sets of pulses, and the distance it travelled to work out the relative velocity.
If the time in between the pulses increases the asteroid is…
moving away from earth
Relative velocity ->
v = increase in distance / time interval
v/c = tback- tout/ tback +tout
Doppler shift
- Doppler uses continuous waves instead of pulses
- The wavelength of the return signal is changed
- If V
Doppler shift
Two-way: wavelength changed out and back
change in λ/ λ = 2(v/c)
One-way: wavelength changed half as much
change in λ/ λ = (v/c)
-The relative velocity calculated from difference between observed wavelength and source wavelength
From the inverse square law…
An object twice as far away will look a quarter as bright; ten times as far will look a hundred times less bright
Mass of black hole
M = V^2 r / G
Evidence that the universe has evolved from an initial uniform, hot dense state comes from…
the existence of the cosmic microwave background
Light intensity to approximate distances between us and stars…
- Can we mimicked in a lab with a light box, a lux meter and measuring ruler.
- Taking measurements and plotting them reveals the linear relationship between light intensity and the reciprocal of the distance squared.
- They are in fact proportional to one another
Problems with measuring light intensity
- We don’t know how bright the stars really are
- We assume that light intensity is not affected by different mediums (including the atmosphere)
Measuring distance using parallax
parallax angle = a + b/ 2
.- This method is only really usable over
relatively short distances.
The Parsec
-A parsec, or 1 pc, is a unit of distance. It is defined as the
distance between the Sun and an object when the parallax
angle is equal to one second of arc
-Distance (in pc) = 1/ Parallax Angle
(when the angle is measured in seconds of arc)
Relative velocity
To determine ∆λ the black lines in the emission spectrum that are absorbed by abundant elements in space (H and He) are tracked, and the movement of the pattern of lines, from what we know to be the true values from experiments on Earth, is used to determine how much the wavelength of the radiation has changed.
Hubble constant
H0 = v/r = 1/ time
-This time is the reciprocal of the Hubble constant time 1/ H0 = elapsed since all galaxies in one place.
Problems with Hubble’s constant
− This assumes that the speed is constant for a galaxy. Due to gravity it isn’t
which gives an over-estimate on the age of the universe.
− H0 is not precisely known.
Hubble’s constant, expansion of the universe
If H0 is low then this implies an old universe (about 20 Gyr). But this data is not what most sources currently obtain. It is increasingly popular to think that H0 is high (say 85) giving a 14 Gyr old universe.
Cosmological Red-Shift
As light travels from one galaxy to another, the universe expands, which stretches the wavelength of the light (or other radiation). This causes a red-shift of the radiation which should not be confused with the red-shift caused by the relative motion of two Distance to galaxy Speed of recession objects (which is known as the Doppler effect).
A red shift
z = change in λ/ λ corresponds to an expansion in scale of
R2/ R1 = 1 + z
The fact that everything measured shows a ∆λ > 0 indicates that the distances between every pair of objects is increasing and that the universe is expanding.
Cosmic Microwave Background Radiation
A temperature fall is observed because as λ gets longer, f gets lower, so by E = hf, E gets lower, and E ∝ T giving a temperature fall. Today (14 Gyr later) the λ is 1mm
(microwaves) and T = 2.7 K. This is also considered to be evidence for the Big Bang.
Energy of a photon
E= fh
where f = frequency of radiation
h= planks constant
Olber’s Paradox
This is a thought-experiment that suggests that if the Universe is infinite then everywhere you looked in the sky your line of sight would (eventually) end with a star, giving a white sky. Olber found that the sky was black rather than white. He claimed that there were not enough stars for an infinite Universe, so it must be finite.
The intensity of the star is …
I ∝ 1/ R*2
