astrophysics

• the cassegrain arrangement (reflecting telescope) uses a parabolic concave primary mirror and a convex seconary mirror
• a concave parabolic mirror will bring parallel light to a point focus.
• chromatic aberration occurs when light of different wavelengths refract to different foci. this results in an image with coloured fringes
• off-axial rays for a spherical mirror are brought to a focus closer to the mirrors, thus means that the focal point is different for different rays of light. this results in a blurred image and is called spherical aberration
• -ve of reflecting telescope:

  secondary mirror and 'spider' holding is in place both diffract the light as it passes, leading to poorer quality image

  some refraction and therefore chromatic aberration eventually, in the eyepiece used to view the final image
• the resolving power of any optical instrument is an indication of how good it is at distinguishing two objects close to one another
• when light from an object enters a telescope through an aperture it is diffracted. this diffraction causes the image to spread out
• when light passes through a small aperture it doesn't produce a bright dot but rather an interference pattern due to diffraction. the centra maxima is a diffuse circular disk called an Airy Disk. the Airy Disk is twice as wide as the further maxima in the pattern
• diffraction affects how well a telescope can resolve fine detail. how much detail the telescope can show is called its resolution
• the Rayleigh Criterion:

  'two objects will be just resolved if the centre of the diffraction pattern of one image coincides with the first minimum of the other'
• the minimum angular resolution of an instrument is the smallest angular separation at which an instrument can distinguish two points

  𝜃 ≈ λ/D
• the rate at which useful energy is received by a telescope is known as its collecting power

  collecting power ∝ (dish diameter)^2
• a larger dish/mirror collects more energy from an object in a given time, giving a more intense, brighter image. this, therefore, means that the telescope can observe fainter objects
• the quantum efficiency (QE) of a detector is the ratio of the number of photons falling on a decide that produce a signal to the total number of photons falling on the device

  QE = detected/incident x100
• the luminosity of an object is the total amount of energy emitted from it per second (the power output), at all wavelengths, measured in watts
• the intensity of an object is the power received from it per unit area on Earth, measured in watts per metre squared. this is the effective brightness on an object
• brightness is a subjective property.

  it depends on the distance of the receiver from the power source
• Intensity follows an inverse square law

  assumptions made: the star is spherical and that it radiates an even amount of power in all directions

  $I=$$P/4πd^2$
• the Hipparchus scale is a non-linear scale that classifies astronomical objects by their apparent magnitudes
• apparent magnitude is a measure of brightness of a star as seen from earth and depends on a star's luminosity and distance from the earth
• on the Hipparchus scale, the brightest stars have an apparent magnitude of 1, the dimmest visible stars have a magnitude of 6
• the intensity of a magnitude 1 star is 100 times greater than a magnitude 6 star
• a difference of 1 on the magnitude scale is equal to an intensity ratio of 2.51
• the brightness ratio between two stars can be calculated through

  $I2/I1 ≈2.51 ^ (m1-m2)$
• a lower apparent magnitude indicates a brighter star
• the absolute magnitude, M, of an object is what its apparent magnitude would be if it were 10 parsecs away from earth
• absolute magnitude is independent of an object's distance from earth
• the astronomical unit (AU) is the mean distance from the sun to the earth

  1AU = 1.50x10^11 m
• the light year (ly) is the distance travelled by light in a vacuum in one year

  1 light year = 9.46x10^15 m
• the parsec (pc) is the distance from which 1AU subtends an angle of 1 arc second

  1pc = 3.08x10^16m = 3.26ly
• 1 arc second = ($1/3600$)°
• parallax is the effect whereby the position or direction of an object appears to differ when viewed from different positions
• the parsec is an important unit because of the way distances to nearby stars can be determined - trigonometrical parallax
• the greater the angle of parallax the closer the object is to you - method only works for nearby objects

  $d ≈r/θ$

  in cases where the angle of parallax is in arc seconds $d ≈1/θ$
• a black-body is a body that is a perfect absorber of radiation (absorbs 100% of radiation incident, at all wavelengths). it therefore emits a continuous spectrum of wavelengths
• a peak of a black-body curve shifts to shorter wavelengths at higher temperatures
• Wien's displacement law states that the wavelength at peak intensity is inversely proportional to the absolute temperature of the object
• assumptions made for Wien's law are :

  the star is a black body, the star has a uniform surface temperature
• it can be seen from Stefan's law that the power output of a black body is proportional to the fourth power of its absolute temperature
• stars are divided into groups called spectral classes. the spectral class of a star depends on its surface temperature