ASTR Midterm 1

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ASTR Midterm 1
2015-07-23 21:07:27
astronomy equations
Deriving formulas from given information
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  1. Given distance to object and object's disk in degree
    Asked to find diameter of object

    convert degree to arcsec
  2. Given semi-major axis of object orbiting the Sun
    Asked to find sidereal period

    • Semi-major axis must be in AU
    • sidereal period in seconds
  3. Given objects length (diameter) and angle it subtends
    Asked to find distance to object

    angle in arcsec
  4. Given mass of object (or ratio of mass) and semi-major axis
    Asked to find gravitational force

    Mass in kg and radius in meters
  5. Given force and object's mass
    Asked to find acceleration

    acceleration in meters/second
  6. Given sidereal period and semi-major axis of exoplanet
    Asked to find mass of star (allowed to assume mass of planet is negligible)

    • a (semi-major axis) in meters
    • P (sidereal period) in seconds
  7. Given objects distance from Sun and perihelion and aphelion
    Asked to find sidereal period

    • sidereal period in seconds
    • semi-major axis in AU
  8. Given perihelion and aphelion
    Asked to find eccentricity of object's orbit
    e ⋅ a= semi-major axis - perihelion

    a is semi-major axis in AU
  9. Given exoplanet's mass and diameter
    Asked to determine weight on planet

    • weight is force
    • most likely asked to compare and set up ratio
  10. Given surface temperature star
    Asked to wavelength star radiates the most energy

    λ in meter
  11. Given surface temperature and radius of star
    Asked to find luminosity

    R in meters
  12. Given frequency of wave 
    Asked to find wavelenght
  13. Given wavelength of wave or photon
    Asked to find energy of wave or photon
  14. Given frequency of wave or photon
    Asked to find energy of wave of photon
  15. Given semi-major axis and period of planetary satellite
    Asked to find mass of planet (not satellite)

    • P is seconds
    • a in meters
  16. Given stellar luminosity and semi-major of orbiting planet
    Asked to find flux of star at planet

    • L in watts 
    • d in meters
    • F in W/m2
  17. Given observed wavelength and laboratory wavelength
    Asked to determine is star is moving toward or away from observer
    Δλ=λobserved - λlaboratory

    • Δλ is positive it is a redshift (moving away)
    • Δλ is negative it is a blueshift (moving toward)
  18. Given observed and laboratory wavelengths
    Asked to determine velocity
  19. Given diameter of telescope
    Asked to find light gathering power
    light gathering power = d
  20. Given diameter of telescope and wavelength of light
    Asked to find resolving power
    θ=2.5×105 (λ÷D) 

    • θ in arcsec
    • λ in meters
    • D in meters
  21. Given resolving power of telescope and distance to observable object
    Asked to determine size of smallest features the telescope can resolve

    α in arcsec
  22. Given surface temperature
    Asked to find flux
    F = σT4

    F in W/m2
  23. Given energy of wave or photon
    Asked to find wavelength
  24. Given luminosity and % mass converted to energy
    Asked to determine mass that is converted to maintain luminosity
    Three parts:

    • Part one: Luminosity is measured in W which = J/s (convert is needed or just make connection)
    • Part Two
    • Part Three: divide mass of part two by % mass
  25. Given parallax
    Asked to determine distance from us

    • p in arcsec
    • d in parsec
  26. Given distance and proper motion
    Asked to find tangential velocity
    vt = 4.74μd

    • μ in arcsec per year
    • d in km
    • vt in km/s
  27. Given observed and laboratory wavelength
    Asked to find radial velocity
  28. Given radial velocity and tangential velocity
    Asked to find space velocity
  29. Given apparent brightness compared to Sun's and distance
    Asked to find luminosity of star
  30. Given star's distance and comparative brightness to star seen without telescope
    Asked for distance to be seen without telescope
  31. Given apparent magnitude of star and two telescope diameters
    Asked to determine magnitude of dimmest star seen through larger telescope
    Two Parts:

    • Part One: Compare light gathering power to get ratio of brightness between viewed stars
    • Part Two:
  32. Given apparent magnitude and parallax
    Two parts:

    • Part One: 
    • Part Two:
  33. Given absolute magnitude of star (star1) and a ratio of luminosity 
    Asked to find absolute magnitude of another star (star2)
  34. Given apparent magnitude and absolute magnitude
    Asked to find distance to star
  35. Given semi-major axis and sidereal period of binary star system
    Asked to find sum of masses of two stars

    Masses in solar mass
  36. Given age of star cluster
    Asked to find mass of turn off star