Astrophysics

• Supernovae are not on the HR diagram because the absolute magnitude is too bright (-19.3) so it goes beyond the scale of HR diagram. It varies in magnitude too so cannot be assigned a position. The temperature of supernovae is too high (50,000K) so doesn't fit on diagram
• Black holes cannot be on HR diagram as escape velocity is greater than speed of light so no light is emitted so the absolute magnitude is too dim to fit on the scale. The temperature of a black hole would be too low (less than 2500K) to be detected by the HR diagram.
• Converging lens makes parallel rays converge to a focus- the point where the parallel rays are focused is called the principal focus or focal point
• Diverging lens makes parallel rays diverge. The point where the rays appear to come from is the principal focus or focal point
• the plane on which parallel rays are incident on the mirror or lens is the focal plane

  The intersection of the focal plane is the focal point
• 1/f = 1/u + 1/v

  Where f= focal length, u= distance from the lens and v= distance from the image
• Image is same side as object is a virtual image and if on opposite side, it is real
• If image arrow is larger it is magnified, if it is smaller then it is diminished
• If the image is on opposite side of principal axis it is inverted, but on same side is upright
• to make a simple refracting telescope- two converging lenses of different focal lengths are needed
• Lens with longer focal length is objective because it faces the object
• By adjusting the position of the inner tube in the outer tube, the distance between the two lenses is altered until the image of distant object is seen in focus
• Simple Refracting telescope- objective lens focuses light ray to form real image of an object, whilst the eyepiece gives the viewer a magnified view of the real image with or without tracing paper. Without tracing paper- viewer sees magnified view of real image but brighter
• Angular magnification- distant object- 3 times larger, angular magnification is 3-angle subtended to naked eye is 1 degree, the angle subtended by telescope would be 3 degrees
• The angular magnification of telescope in normal adjustment= angle subtended by final image at infinity to the viewer / angle subtended by distant object at unaided eye = β / α
• Stars are so far away they are effectively point objects- when viewed through a telescope the stars seem to be brighter, as the telescope objective is wider than pupil. Pupil of eye is about 10mm
• Better telescopes have bigger apertures
• Cassegrain reflecting telescope- concave mirror instead of a converging lens. Concave mirror- primary mirror, secondary smaller mirror reflect light from convex reflector into the eye piece.
• Cassegrain reflecting telescope- light from distant object it

  • Reflected by concave mirrr
  • Reflected by the convex mirror onto small hole at centre of concave mirror into eyepiece
  • Refracted by eyepiece into a parallel beam which enters viewer’s eye.

  So viewer will see a virtual image at infinity
• Primary mirror of Cassegrain telescope should be parabolic- reduce spherical aberrations
• Angular separation- extent of detail that can be seen in a telescope image depends on width of the objective
• The telescope resolves two stars- if objective is too narrow, the stars would overlap so they would not be seen as separate stars
• Diffraction at a circular aperture can be observed on a screen through a small circular pasture before reaching the screen
• Rayleigh criterion - least angular separation is given by lander/d (MUST BE IN RADIANS)
• Telescopes on earth have images that are slightly smudged because there is refraction by the atmosphere due to the movement of air
• Whe working with parsec- must use RADIANS
• Luminosty of a star the amount of energy it casually radiates per second
• Intensity- power per unit area at the observer
• Apparent magnitude- the brightness of a star as seen from the naked eye at earth. Hipparcos scale - 1-> 6 where 1 is brightest and 6 is dimmest
• A star with apparent magnitude 1 is 2.5x brighter than a magnitude 2 star
• Absolute magnitude is what an object’s apparent magnitude would be if it were 10 parsecs away from Earth
• A black body is a body that absorbs all electromagnetic radiation of all wavelengths and can emit all wavelengths of electromagnetic radiation
• Black bodies are effect emitters and absorbers of radiation
• We assume all stars are black body stars
• Black body curves show peak wavelengths of stars- hotter the star, shorter the peak wavelengths
• Wien’s Law- wavelength at peak intensity is inversely proportional to the absolute temperature of the object

  Peak wavelength x Temperature (K) = 0.0029 m K
• Stefan’s Law- total energy per second emitted by a black body at absolute temperature T is proportional to its surface area A an T^4 as

  P= sigma x A x T^4
• Two stars- same absolute magnitude- same power output so if surface areas are equal, they must have same radius. If surface temperatures are unequal, the cooler tr must have the bigger radius
• Intensity = power / 4pi x distance^2

  So a star at 3 times distance will appear 9 times less intense
• Supernovae are objects which exhibit rapid and enormous increase in absolute magnitude (-14.3 - -19.3)