Sample Questions: Astrophysics test#1

 

I. Astronomical coordinate systems and nomenclature:

  1.  How many degrees in an hour of right ascension?
  2. At latitude 32 degrees north, is a star with declination +58 degrees circumpolar? What about a star with a declination –32 degrees?
  3. What point in the sky fixes the zero hour of right ascension?  What does it have to do with the seasonal position of the sun?
  4. Gamma Andromedae is a star in the constellation Andromeda.  Is it a relatively bright star compared to the other stars in the constellation? How can you tell?
  5. An astronomer casually mentions working on SX Arietis.  What kind of object is he studying?

 

II. Basic Mechanics:

  1. A particle of mass 2kg has a velocity of 2i+3j m/s when it is at r=5i+0j m.  Find the angular momentum of the particle.
  2. Prove that for any central force the angular momentum L is conserved. 
  3. Show that for a circular orbit around a planet the tangential velocity of a mass m must be vc=(G M/r)1/2 where M is the mass of the planet.
  4. Show that in a circular orbit the total energy, given by the sum of the KE and the PE, is just –GMm/(2r)
  5. Prove, using energy conservation, that escape velocity vesc is 1.4 vc given above.

 

III. Celestial mechanics:

  1. Fill in the following table:

 

 

planet

Distance (A.U.)

T (years)

Vc (km/s)

Mercury

0.39

 

 

Venus

0.72

 

 

Earth

1.0

 

 

Mars

 

1.52

 

 

Jupiter

5.2

 

 

 

 

  1. Kirkwood gaps occur in the asteroid belt whenever the orbital period of an asteroid falls at an integer fraction of Jupiter’s period.  Find the distances from the sun of the gaps due to the ½ , 1/3, 2/3, and ¼ resonances  Compare these distances to the orbital radii of Mars and Jupiter’s orbits.

 

 

  1. A rocket launched from earth reaches an altitude of 100 km above the earth’s surface moving at 7 km/s at an angle of 5o above the horizontal.  Find E and L for these initial conditions, then find a and e for this orbit.  Does the rocket go into a safe orbit or does it eventually strike the surface of the earth?  Justify your answer.
  2.  A binary star consists of a white dwarf, Rwd=6000 km, and a companion star Rs=400,000 km.  If the white dwarf has a mass Mwd=0.7 Msun and the companion has a mass 0.35 Msun and their centers are separated by 1 million km, find the period of the orbit of the stars.  Find the distances of each star’s center from the center of mass of the system.  Find the velocities of each star assuming a circular orbit for each.

 

IV. Basic radiation laws:

  1.  What is the flux in Watts/m2 emitted from the “surface” of the sun (Rsun =700,000km and Tsun=5800 K)?
  2. What is the flux of radiation from the sun at the distance of the Earth, r =1.49x1011m?

17.  Calculate the equilibrium temperature of a rotating spherical planet orbiting at the distance of mercury from the sun (assuming a perfect blackbody). At what wavelength does such a planet radiate most of its energy?

  1. In the solar system find the distances from the sun where liquid water can exist on a rotating planet radiating like a blackbody.  Compare this region to the orbital distances of Venus, Earth, and Mars from the sun.  How do planetary atmospheres affect these results?
  2.  In the white dwarf binary system in the last section, the temperature of the white dwarf is about 100,000 K while the companion star is about 3000K.  The stars are tidally locked so one hemisphere of the companion is irradiated by the white dwarf continuously.  Estimate the equilibrium temperature of the side of the companion facing the white dwarf neglecting albedo effects.  This heating is called the “reflection” effect.