Be careful of units and use appropriate
precision. Be sure to explain your reasoning on each problem, so you can
get partial credit for your work. Answers without explanations are not
acceptable. You are encouraged to work together, but please write this
up yourself. 1) Think up your own
outrageous estimation of some very large or small number (like how many
drops are in the ocean), then do the estimation. Be sure to state your
assumptions and estimations along the way, and keep track of units. Alternatively
(if you aren't feeling creative), estimate the number of cells in your
body. Be sure to explain each of your assumptions along the way and justify
them.
Throughout the term,
we will be asking some questions about a fictitious planetary system and
Galaxy. We will tell you things about it as needed and you will slowly
build up a picture of what it is like as we go along. We hope you will
have some fun trying to figure out what this new place is like.
We start with a planet
going around a star (which we will call the Son). This is the planet Astra,
and the inhabitants are the Astroids. What you need to know about Astra
right now is that its equator lies in its orbital plane (or put another
way, its spin axis is aligned with its orbital axis). It also spins the
same direction as it orbits (like the Earth). Two of the major cities on
Astra are Meridio, which is at the equator, and Dimmlee, which is at the
south pole. The Astral year is exactly 180 Astral days long. By great fortune,
the units of time and distance are the same as ours, unless we explicitly
say otherwise (so days, hours, minutes, and seconds are the same, but the
year is different).
2) Describe the apparent
daily motion of the Son through the sky as seen from Meridio, then from
Dimmlee. How do these change throughout the Astral year?
3) Where does Astra's
ecliptic lie in terms of Astra's celestial coordinate system? On New Year's
day, the Son appears on the celestial equator. Where does it appear 90
days later?
4)You
have a Mark III HoverCar, which travels at a blistering 200 km/hr. You
travel due south for 5 hours, until the north celestial pole appears 10
degrees closer to the horizon than when you started. What is the radius
of Astra (in km)?