Midterm 1 Solutions

Released solutions for Midterm 1

Author

Dr. Anna Rosen

These brief solutions are meant to help you check both your answers and your reasoning. A recurring theme in this exam is the difference between what astronomers directly measure and what they infer from models, geometry, and physical laws.

Answer Key

Q Ans Q Ans Q Ans Q Ans Q Ans
1 A 6 B 11 B 16 C 21 B
2 D 7 D 12 C 17 D 22 A
3 C 8 A 13 C 18 C 23 B
4 B 9 B 14 D 19 A 24 D
5 A 10 A 15 C 20 A 25 D

Brief Solutions

  1. A. Opposite seasons in opposite hemispheres show that seasons come from Earth’s axial tilt, which changes Sun angle and daylight length by hemisphere.
  2. D. ISS astronauts float because they and the station are in free fall together around Earth, not because gravity disappears.
  3. C. Wien’s law says temperature is inversely proportional to peak wavelength, so a 500 nm peak means twice the temperature of a 1000 nm peak.
  4. B. The telescope directly records a wavelength shift in spectral lines; radial speed is inferred from that shift.
  5. A. The Moon’s orbit is tilted, so most new Moons are not lined up precisely enough to produce a solar eclipse.
  6. B. For a Sun-like star, Kepler’s third law gives (P^2 = a^3), so (P^2 = 4^3 = 64) and (P = 8) years.
  7. D. Doppler shift measures only motion toward or away from us, so purely sideways motion gives zero radial Doppler shift.
  8. A. The shorthand (P^2 = a^3) is a special Solar-System-style form; the full relation depends on the central mass and constants.
  9. B. Different elements absorb and emit at specific wavelengths, so spectral lines reveal composition.
  10. A. Apparent brightness follows the inverse-square law, so a star four times farther away looks (1/4^2 = 1/16) as bright.
  11. B. During a lunar eclipse, Earth’s atmosphere scatters blue light more strongly and bends redder light into the shadow.
  12. C. Kepler described orbital patterns from observation, while Newton explained those patterns with gravity.
  13. C. Flat rotation curves show outer stars moving too fast for visible matter alone, implying additional unseen mass.
  14. D. Apparent brightness is directly measured at the telescope; temperature, mass, and distance are inferred.
  15. C. At the same temperature, luminosity scales as (R^2), so tripling the radius makes the star (3^2 = 9) times as luminous.
  16. C. Gravitational force scales with the orbiting object’s mass, so a planet with (3m) feels three times the force at the same distance.
  17. D. A cool gas cloud in front of a bright continuous source produces dark absorption lines at specific wavelengths.
  18. C. Constellations are line-of-sight sky patterns, so their stars can lie at very different distances from Earth.
  19. A. Gravity follows an inverse-square law, so doubling distance reduces force to (1/4) of its original value.
  20. A. Large astronomical distances are inferred from evidence such as brightness, standard candles, or redshift, not directly seen as a ruler measurement.
  21. B. Using (c = f), the wavelength is (= c/f = (3 ^8 )/(3 ^8 ) = 1 ).
  22. A. With equal luminosity, (L R^2 T^4). Doubling temperature increases (T^4) by (2^4 = 16), so (R^2) must decrease by 16, which means the radius becomes one-quarter as large.
  23. B. Moon phases are the normal changing Sun-Earth-Moon geometry, while eclipses require special alignment near the Moon’s orbital nodes.
  24. D. Kepler’s second law says a planet moves fastest when it is closest to the Sun, where it sweeps out equal areas in equal times with the shortest lever arm.
  25. D. Shorter wavelength means higher photon energy, so the 1 nm X-ray photon carries the most energy.