Scaling & Daily Motion

Scaling Often one is interested in how quantities change when an object or a system is enlarged or shortened Different quantities will change by different factors! Typical example: how does the circumference, surface, volume of a sphere change when its radius changes?

How does it scale? Properties of objects scale like the perimeter, the area or the volume –Mass scales like the volume (“more of the same stuff”) –A roof will collect rain water proportional to its surface area

Daily Rising and Setting Due to the rotation of the Earth around its axis Period of rotation: 1 siderial day= 23 h 56 m 4.1 s 1 solar day (Noon to Noon) = 24 h Stars rotate around the North Star – Polaris

What time is it? Depends on where you are on the Earth! Time zones ensure that the noon is really noon, i.e. sun is at highest point To avoid confusion, use universal time (UT), the time at the meridian in Greenwich UT = EST + 5 hrs Daylight savings adds one hour in spring, so UT = EDT+ 4 hrs

The Time Zones Established to insure that sun is at highest point approximately at noon in the middle of the time zone

Daily and yearly motion intertwined Solar vs Siderial Day –Earth rotates in 23 h 56 m –also rotates around sun  needs 4 min. to “catch up” Consequence: stars rise 4 minutes earlier each night (or two hours per month, or 12 hours in ½ year)  After 1/2 year we see a completely different sky at night!