ASTR Midterm 1

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  1. Given distance to object and object's disk in degree
    Asked to find diameter of object
    chart?chf=bg,s,00000000&cht=tx&chl=D%20%3D%20%5Cfrac%20%7Ba%20%5Ccdot%20d%7D%20%7B206265%7D&chs=166x66

    convert degree to arcsec
  2. Given semi-major axis of object orbiting the Sun
    Asked to find sidereal period
    chart?chf=bg,s,00000000&cht=tx&chl=P%5E2%20%3D%20a%5E3&chs=120x36

    • 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
    chart?chf=bg,s,00000000&cht=tx&chl=D%20%3D%20%5Cfrac%20%7Ba%20%5Ccdot%20d%7D%20%7B206265%7D&chs=166x66

    angle in arcsec
  4. Given mass of object (or ratio of mass) and semi-major axis
    Asked to find gravitational force
    chart?chf=bg,s,00000000&cht=tx&chl=F%20%3D%20%5Cfrac%20%7BG%20%5Ccdot%20m_1%20%5Ccdot%20m_2%7D%20%7Br%5E2%7D&chs=202x70

    Mass in kg and radius in meters
  5. Given force and object's mass
    Asked to find acceleration
    chart?chf=bg,s,00000000&cht=tx&chl=F%20%3D%20m%5Ccdot%20a&chs=130x28

    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)
    chart?chf=bg,s,00000000&cht=tx&chl=P%5E2%3D%20%5Cfrac%20%7B4%20%5Ccdot%20(pi)%5E2%20%5Ccdot%20a%5E3%7D%20%7BG(m_1%20%2B%20m_2)%7D&chs=238x90

    • 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
    chart?chf=bg,s,00000000&cht=tx&chl=P%5E2%20%3D%20a%5E3%20&chs=120x36

    chart?chf=bg,s,00000000&cht=tx&chl=a%3D%20%5Cfrac%20%7Bperihelion%20%2B%20aphelion%7D%20%7B2%7D&chs=364x72

    • 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
    chart?chf=bg,s,00000000&cht=tx&chl=W%3D%20%5Cfrac%20%7BG%20%5Ccdot%20m%20%5Ccdot%20M_p_l%7D%20%7B(r_p_l)%5E2&chs=220x86

    • 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
    chart?chf=bg,s,00000000&cht=tx&chl=wavelength_m_a_x%3D%5Cfrac%7Bconstant%7D%7BT%7D&chs=396x64

    λ in meter
  11. Given surface temperature and radius of star
    Asked to find luminosity
    L=4⋅(pi)⋅R²⋅σ⋅T4

    R in meters
  12. Given frequency of wave 
    Asked to find wavelenght
    chart?chf=bg,s,00000000&cht=tx&chl=v%3D%5Cfrac%20%7Bc%7D%7Bwavelength%7D&chs=224x66
  13. Given wavelength of wave or photon
    Asked to find energy of wave or photon
    chart?chf=bg,s,00000000&cht=tx&chl=E%3D%5Cfrac%7Bh%20%5Ccdot%20c%7D%7Bwavelength%7D&chs=234x74
  14. Given frequency of wave or photon
    Asked to find energy of wave of photon
    chart?chf=bg,s,00000000&cht=tx&chl=E%3Dh%20%5Ccdot%20v&chs=120x28
  15. Given semi-major axis and period of planetary satellite
    Asked to find mass of planet (not satellite)
    chart?chf=bg,s,00000000&cht=tx&chl=P%5E2%3D%20%5Cfrac%20%7B4%20%5Ccdot%20(pi)%5E2%20%5Ccdot%20a%5E3%7D%7BG(m_1%20%2B%20m_2)%20&chs=238x90

    • P is seconds
    • a in meters
  16. Given stellar luminosity and semi-major of orbiting planet
    Asked to find flux of star at planet
    chart?chf=bg,s,00000000&cht=tx&chl=F%3D%20%5Cfrac%7BL%7D%7B4%20%5Ccdot%20(pi)%20%5Ccdot%20d%5E2%7D&chs=188x78

    • 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
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%20%7Bv%7D%7Bc%7D%20%3D%20%5Cfrac%20%7Bwavelength_o_b_s_e_r_v_e_d%20-%20wavelength_l_a_b%7D%20%7Bwavelength_l_a_b&chs=534x80
  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
    chart?chf=bg,s,00000000&cht=tx&chl=D%3D%20%5Cfrac%20%7Ba%20%5Ccdot%20d%7D%7B206265%7D&chs=166x66


    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
    chart?chf=bg,s,00000000&cht=tx&chl=E%3D%20%5Cfrac%20%7Bh%20%5Ccdot%20c%7D%7B%20wavelength%7D&chs=234x74
  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 Twochart?chf=bg,s,00000000&cht=tx&chl=E%3D%20m%20%5Ccdot%20c%5E2&chs=142x28
    • Part Three: divide mass of part two by % mass
  25. Given parallax
    Asked to determine distance from us
    chart?chf=bg,s,00000000&cht=tx&chl=d%3D%20%5Cfrac%20%7B1%7D%7Bp%7D&chs=84x64

    • 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
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%20%7Bv_r%7D%7Bc%7D%20%3D%20%5Cfrac%20%7Bwavelength_o_b__s_e_r_v_e_d%20-wavelength_l_a_b%7D%7Bwavelength_l_a_b&chs=546x80
  28. Given radial velocity and tangential velocity
    Asked to find space velocity
    chart?chf=bg,s,00000000&cht=tx&chl=v%3D%20%5Csqrt%20%7Bv_t%5E2%2Bv_r%5E2%7D&chs=186x58
  29. Given apparent brightness compared to Sun's and distance
    Asked to find luminosity of star
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%20%7BL_s_t_a_r%7D%7BL_s_u_n%7D%20%3D%20(%5Cfrac%20%7Bd_s_t_a_r%7D%7Bd_s_u_n%7D)%5E2%20%5Ccdot%20(%5Cfrac%7Bb_s_t_a_r%7D%7Bb_s_u_n%7D)&chs=314x76
  30. Given star's distance and comparative brightness to star seen without telescope
    Asked for distance to be seen without telescope
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%20%7BL_1%7D%7BL_2%7D%20%3D%20(%5Cfrac%7Bd_1%7D%7Bd_2%7D)%5E2%20%5Ccdot%20(%5Cfrac%7Bb_1%7D%7Bb_2%7D)&chs=220x76
  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:
    •  chart?chf=bg,s,00000000&cht=tx&chl=m_2-m_1%3D2.5log(%5Cfrac%7Bb_1%7D%7Bb_2%7D)&chs=312x76
  32. Given apparent magnitude and parallax
    Two parts:

    • Part One: 
    • chart?chf=bg,s,00000000&cht=tx&chl=d%3D%5Cfrac%7B1%7D%7Bp%7D&chs=84x64
    • Part Two:
    • chart?chf=bg,s,00000000&cht=tx&chl=m-M%3D5log(d)-5&chs=296x38
  33. Given absolute magnitude of star (star1) and a ratio of luminosity 
    Asked to find absolute magnitude of another star (star2)
    chart?chf=bg,s,00000000&cht=tx&chl=M_1-M_2%3D2.5log(%5Cfrac%7BL_1%7D%7BL_2%7D)&chs=338x76
  34. Given apparent magnitude and absolute magnitude
    Asked to find distance to star
    chart?chf=bg,s,00000000&cht=tx&chl=m-M%3D5log(d)-5&chs=296x38
  35. Given semi-major axis and sidereal period of binary star system
    Asked to find sum of masses of two stars
    chart?chf=bg,s,00000000&cht=tx&chl=M_1%2BM_2%3D%5Cfrac%7Ba%5E3%7D%7BP%5E2%7D&chs=228x70

    Masses in solar mass
  36. Given age of star cluster
    Asked to find mass of turn off star
    chart?chf=bg,s,00000000&cht=tx&chl=t%3D%20%5Cfrac%7B1.2%20%5Ccdot%2010%5E1%5E0years%7D%7BM%5E2%5E.%5E5&chs=236x82
Author:
nikachan
ID:
305620
Card Set:
ASTR Midterm 1
Updated:
2015-07-24 01:07:27
Tags:
astronomy equations
Folders:
science,equations,midterm
Description:
Deriving formulas from given information
Show Answers: