Knowledge-22 SAC

• The astronomical unit (AU) is the average distance from the earth to the sun:

  • 1 AU =1.5x10^11
• The light year is the distance travelled by light in a vacuum in a year:

  • 1 ly = 3x10^8 x (365x24x60x60)
  • 1 ly = 9.46x10^15
• Parallax is where the closer an object is to the viewer the faster it moves.
• A parsec is the distance to a star that subtends an angle of one second at a distance of 1 AU.
• luminosity is the total power radiated by a star.
• intensity is the power radiated per unit area at the observer.
• Brightness is a subjective scale of measurement ; how bright a star appears depends on both its distance and the power emitted at visible wavelengths . Brightness is measured n the Hipparchus scale. The faintest star visible with the naked eye from earth has a value of 6 ; the brightest is one.
• Apparent magnitude;

  the brightness of an astronomical body as seen from earth. An observer receives 100 times more light from a star with m = 1 than m = 6 . A difference of 1 is equal to an intensity ratio of 2.51. Stars can have a negative value m
• Absolute magnitude:

  The apparent magnitude an astronomical body would have if it was 10 pc from the observer with d in pc:

  • m-M = 5 log10 (d/10)
  • d < 10 pc , m<M
  • d > 10 pc , m> M
• Transits- light curves show decrease / periodic variation in apparent magnitude.
• radial velocity- orbiting planets cause stars to wobble , and light is blue and red shifted.
• Hubbles law states that the universe is expanding - all galaxies are moving away from each other . with :

  • v = Hd
  • H = Hubble constant
• 1/H is approximate age of universe
• Evidence for the big bang comes from Hubble's law , supported by cosmic microwave background radiation and helium production in the early universe.
• Quasars:

  • emit all types of EM radiation
  • come from supermassive black holes in the centre of galaxies.
  • have very large powers
• Doppler effect:

  The frequency and wavelength detected depend on the relative velocity of the observer.

  • change in f / f = v/c
  • red shift := change in wavelength / frequency = -v/c
• Stefan's law:

  • l max T = 2.9x10^-3 mk
  • T in kelvins
  • hotter stars appear white/blue , cooler stars appear red
• Wiens displacement law:

  • P = sAT^4
  • T in kelvin and A in m^2
  • if star x and star y are at the same temperature , X will appear brighter if it has a larger area than y
  • Px / Py = Ax /Ay (Tx/Ty)^4
• Supernovae show a sudden, huge increase in magnitude over days and are billions of times brighter than the sun. Type 1a supernovae are used as standard candles to work out distances , using the inverse square law.
• Neutron stars are made of neutrons, are small with a huge density , similar to that of atomic nuclei.
• Black holes have escape velocity which defines the event horizon : this implies a radius of Rs = 2GM / c^2 . They can produce gamma rays burst during formation and probably exist as supermassive black holes at the centre of galaxies.
• Dark energy could be responsible for the accelerated expansion of the universe.
• Stars are classified by temperatures O (hot , ionized) , B,A,F,G,K,M (cool).

  • above 10,000 K (O-A) - hydrogenis ionized
  • below 10,000 K (A-M) - electrons move up then down by different steps producing dimming = absorption lines.
• Hipparchus scale:

  1

  2 x 2.5

  3 x 6.25

  4 x 16

  5 x 40

  6 x 100
• To find brightness in from the hipparchus scale:

  1. find the difference in hipparchus scale from two points
  2. turn the difference into a power of 2.51
  3. solve
• luminosity is the total power radiated by a star (W)
• Intensity is the power radiated per unit area at the observer (W/m^2)
• Brightness is a subjective scale of measurement , how bright a star appears depends on both its distance and the power emitted at visible wavelength.
• Apparent magnitude is the brightness of an astronomical scale as seen from earth (hipparchus scale).
• Absolute magnitude is the apparent magnitude an astronomical body would have if it was 10pc from the observer.
• How to find absolute magnitude:

  • m - M = 5 ln ( d/10 ) where d is in parsecs
• If d is 10 parsecs then:

  • m-M = 5 ln (10/10)
  • m-M = 5 ln(1)
  • m-M = 0
  • Both magnitudes are equal
• A black body is a body which absorbs all the radiation hitting it
• Black body radiation is a type of e/m radiation which is emitted by a perfect black body which is held at a constant uniform temperature.
• The spectrum peaks at a wavelength that shifts to shorter values at higher temperatures.
• As the body gets hotter , more radiation is emitted ( the total power is proportional to the area under the graph), the spectrum applies to stars aswell.
• Stefan's law states that total power P radiated by a body of surface area A is :

  • P = stefan's constant x surface area x temperature^4
• Wien's law states that:

  • wavelength x temperature = 2.9x10^-3 mK
• light emitted from the sun can produce a characteristic spectrum when viewed through a diffraction grating.
• The absorption lines are produced when light passes through the cooler gases in the outer atmosphere of the sun.