# ASTR Midterm 1

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 Author: nikachan ID: 305620 Filename: ASTR Midterm 1 Updated: 2015-07-23 21:07:27 Tags: astronomy equations Folders: science,equations,midterm Description: Deriving formulas from given information Show Answers:

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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

• 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

Mass in kg and radius in meters
5. Given force and object's mass

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

• 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

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

R in meters
12. Given frequency of wave
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
19. Given diameter of telescope
Asked to find light gathering power
light gathering power = d
20. Given diameter of telescope and wavelength of light
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
F = σT4

F in W/m2
23. Given energy of wave or photon
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
vt = 4.74μd

• μ in arcsec per year
• d in km
• vt in km/s
27. Given observed and laboratory wavelength
28. Given radial velocity and tangential 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

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