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