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Foundations of Astronomy ASTR/PHYS 2500
Exam 1 *
Physical Constants Gravitational constant Elementary charge Vacuum permittivity Electron Volt Speed of light in vacuum Planck constant Reduced Planck constant Boltzmann constant Stefan-­‐Boltzmann constant Proton mass Electron mass Atomic mass unit Mass of an iron atom Astronomical Constants
G e ε0 eV c h h/2π k σSB mp me u or amu mFe -­‐11
6.673 x 10 -­‐19
1.602 x 10 -­‐12
8.854 x 10 -­‐19
1.602 x 10 8
2.998 x 10 -­‐34
6.626 x 10 -­‐34
1.055 x 10 -­‐23
1.381 x 10 -­‐8
5.670 x 10 -­‐27
1.673 x 10 -­‐31
9.109 x 10 -­‐27
1.6605 x 10 -­‐26
9.2731 x 10 3
-­‐1 -­‐2
m kg s C 2 -­‐1
-­‐1
C J m J -­‐1
m s J s J s -­‐1
J K -­‐1
-­‐2 -­‐4
J s m K kg kg kg kg * Mass of Earth Mass of Sun Mass of Moon Equatorial radius of Earth Mean radius of Earth Equatorial radius of Sun Equatorial radius of Moon Mean density of Earth Mean density of Sun Mean density of Moon Jupiter radius Jupiter mass Luminosity of Sun Effective temperature of Sun Light-­‐year Astronomical Unit Parsec Length of solar day Length of sidereal day Length of a year (Julian) 24
5.974 x 10 30
1.989 x 10 22
7.36 x 10 6378 6371 5
6.955 x 10 1737 5515 1408 3346 10.97 317.8 26
3.839 x 10 5778 12
9.461 x 10 8
1.496 x 10 13
3.086 x 10 24 hours = 86400 seconds 23hours 56 minutes = 86160 s 8
3.15576 x 10 kg kg kg km km km km -­‐3
kg m -­‐3
kg m -­‐3 kg m
Mean Earth radii Mean Earth masses W K km km km s ASTR/PHYS 2500 Exam 2 ii
1a. Give at least one piece of evidence or line of reasoning given by Aristotle to argue that the Earth is spherical. 1b. What is meant by a sidereal day? 1c. What are Kepler’s three laws of planetary motion? I. II. III. 1d. In qualitative terms, describe the Roche radius. 1e. Specify the optical depth τ as either << 1, ~1 or >> 1 for visible light pass through these physical objects: the air in this room: τ _______ hot gas in the interior of the Sun: τ ________ fog on an ocean through which you spy the legendary ghost ship The Flying Dutchman: τ _____ 1f. An emission line of hydrogen comes from a hot, optically thin gas. The fractional spread in the wavelength of the line is Δλ/λ = 2x10-­‐5, corresponding to a temperature of T = 5000 K and typical speed of the hydrogen atoms of 7 km/s. What is the temperature T if the line width were double this value? T (K): __________ Would T be higher or lower if the same Δλ/λ were observed in a helium line? ASTR/PHYS 2500 Exam 2 iii
2a. Using the above cartoon of the Celestial Sphere, give a crude estimate of the location of the star (“object”) in the diagram. [Estimate to the nearest hour or 10’s of degrees, for example] right ascension (hours): declination (degrees): 2b. Today is the first day of Fall! On this day here in Salt Lake City (latitude=40.7o N), the sun is highest in the sky at about 1:20 pm Mountain Daylight Time. At roughly what time would the star in part (a) appear to be highest in the sky (closest to zenith)? Time (MDT): ___________________ 2c. Approximately what is the southernmost latitude from which the star in part (a) can be seen? Latitude (degrees S): ______________ ASTR/PHYS 2500 Exam 2 iv
In 1976, an artificial satellite, Helios 2, traveled toward the Sun for a close-­‐in study of our host star. The satellite was put on an eccentric orbit with a perihelion distance of 0.29 AU, the smallest of any orbiting artificial satellite. Its apohelion distance is 0.98 AU, set by its launch point here on Earth. [Source: solarsystem.nasa.gov/missions/profile.cfm?MCode=Helios_02] 3a. Find the period P of Helios 2’s orbit. P (years): ___________ 3c. Suppose Helios 2 was equipped with engines to place it on a circular orbit at 0.29 AU (it wasn’t). Assuming that the Earth is also on a perfectly circular orbit at 1 AU, find the time interval between successive “close” encounters between Helios 2 and the Earth, when the separation between the two is only 0.71 AU. P (years) = _____________ 3b. Assuming that Helios 2 is an ideal, spherical blackbody, approximate its temperature (in Kelvin) if it reaches equilibrium with radiation from the Sun when it is at 0.29 AU. 2
[Hint: the flux (power/unit area) at a distance D from the sun is F=L/4πD . If you need the radius of the satellite, you may assume that it is Rsatellite = 1 m. Note: the spacecraft was far from spherical, and probably nowhere near a perfect blackbody absorber/radiator. Yet the estimate asked here would have been key for Helios’ designers…] T (K) = _____________