1. Parallax Distance with Uncertainty 16 points
A nearby star has measured parallax p = 0.040 arcsec with uncertainty +/-0.004 arcsec. Compute its distance in parsecs and light-years. Estimate the fractional uncertainty in the distance.
Instructions
Show reasoning, units, diagrams or plots where useful, and source acknowledgments. Numerical answers without explanation receive limited credit. Eligible submissions may be revised after feedback.
Concrete Problems
2. Solar-System Scale Model 12 points
In a scale model, Earth is 15 m from the Sun. Neptune is about 30 AU from the Sun. Where should Neptune be placed? If light takes about 8.3 minutes to travel 1 AU, how long does sunlight take to reach Neptune?
3. Kepler's Third Law 14 points
An asteroid orbits the Sun with semi-major axis a = 2.5 AU. Use P^2 = a^3 to estimate its orbital period in years. Show the calculation and interpret why the period is longer than Mars's period but shorter than Jupiter's.
4. Tidal Reasoning 10 points
Tidal effects depend strongly on distance because they come from differences in gravity across an extended body. If the Moon were twice as far from Earth, would the ocean tide-raising effect be slightly smaller, about half, or much smaller? Explain qualitatively.
Recommended OpenStax Practice
- OpenStax Astronomy 2e, Science and Universe / scale exercises, Review Question 8, extracted index line 2674: angular motion of the Sun relative to fixed stars.
- OpenStax Astronomy 2e, Orbits and Gravity exercises, Review Question 1, extracted index line 3826: Kepler's three laws.
- OpenStax Astronomy 2e, Orbits and Gravity exercises, Thought Question 22, extracted index line 3867: forces in circular motion.
- OpenStax Astronomy 2e, Orbits and Gravity exercises, Thought Question 23, extracted index line 3869: satellite orbital speed during inward spiral.