Astronomy 300: Homework Assignment #2

Due: Wednesday February 8

Scale Model

  1. Make a scale model of the Solar System on the First Floor of Thornton Hall, as follows.

  2. Similarly determine the locations for Mercury, Venus & Mars.

  3. A true scale model also requires proportionally sized objects to represent the planets. Compute the ratio of the Sun's diameter (or radius) to Earth's. Round off this number and try to remember it. What object should you use to represent Earth?

    Reading: The Watershed , Ch. 6 and C&O, Ch 2

  4. Kepler modeled Mars' orbit as a circle, with the Sun offset from the Center, around which Mars moved non-uniformly (however as viewed from one point, the Equant, or puntus equans Mars' motion appeared uniform.). After 900 pages of calculations, he finally determined the parameters of this model, eg. the radius of this circle. Why did Kepler then reject the model?

  5. On p. 149 of The Watershed, Koestler states that Kepler "knew his inverse-ratio 'law' (between the planet's speed and distance was incorrect". That is, a planet's velocity is not simply proportional to the reciprocal of its distance from the Sun. How, exactly, does velocity depend on distance? Write down one equation from C&O which gives the relationship between the two.

  6. For a planet with eccentricity e, and semimajor axis a, write expressions for the planet's orbital distance from the Sun at perihelion (rp) and aphelion (ra).

  7. What is the maximum variation (Delta r) in a planet's distance from its host star as a function of a and e? Evaluate this quantity for the Earth (with e=0.017): how much closer to the Sun is Earth at perihelion (Jan. 4th) than aphelion (July 4th)? Express your answer in both km and AU (ie a fraction).

    Reading: Croswell, Ch 2&3

  8. In 1897, Kapteyn discovered a remarkable star. What was special about it and why does it have this property? In 2014, something else interesting was discovered regarding this same star. What?

  9. What mistake did Kapteyn make in his attempt to map the Milky Way? Describe the observations that provided the first hints at what he had overlooked.

  10. Compute the velocity of the Sun's orbit around the Milky Way. Assume a circular orbit. Use the values given in Ch. 1 of Croswell for the Sun's distance from the Galactic center and its orbital period around the Galaxy. Hint: conversion factors, e.g. from lightyears to meters, etc, may be found on the inside front cover of Carroll and Ostlie (Appendix A).