L>y2kcenter.org 113Assignment #1SOLUTIONSChapter 117. Expect you space on a weird planet and observe, at night, that the stars do not rise and set butcircle parallel come the horizon. Currently you to walk in a continuous direction because that 8000 miles, and at her newlocation on the planet you discover that every stars rise straight increase in the east and set straight down in thewest, perpendicular to the horizon.a) How can you determine the circumference of the world without any kind of further observations?c) What is the circumference, in miles, of that planet?Since the stars execute not climb or set, you have to be in ~ the phibìc (or South) pole the the planet. As soon as youwalk come the allude where the stars rise and collection perpendicular come the horizon, you room at the equator ofthe planet. ANSWERa) by walking indigenous the north pole to the equator, you"ve covered 1/4 of the circumference of thesphere (viewed as a circle). Therefore by multiply by 4, you can determine the entirecircumference.c) because the street is 8000 miles, the entire circumference the the planet must be 4 x 8000 miles= 32000 miles.Chapter 214. What is the semimajor axis the a circle of diameter 24cm? What is that is eccentricity?ANSWERA circle of diameter that 24cm has actually a significant axis (from one leaf diametrically across to the various other edge)of 24cm. The semimajor axis is one-half of the significant axis (= 24cm / 2 = 12cm). As you deserve to see,it is simply the radius the the circle and also equal come 12cm. A circle has actually an eccentricity that zero.Chapter 219. What would be the duration of a planet whose orbit has actually a semi-major axis the 4 AU? Of an asteroidwith a semimajor axis that 10 AU? ANSWERAccording come Kepler"s 3rd Law, P2 = D3 whereby P is to express in devices of years and also D in units ofAU. For this reason P = D3/2. For a earth that has actually D = 4 AU, p = (4)3/2 = (4 x 4 x 4)1/2 = (64)1/2 = 8 years.For one asteroid that has actually D = 10 AU, p = (10)3/2 = (10 x 10 x 10)1/2 = (1000)1/2 = 31.6 years.Chapter 39. Where room you ~ above the planet according to the complying with descriptions? (Refer earlier to chapter 1as well together this chapter.)a) The stars rise and set perpendicular come the horizon.b) The stars circle the skies parallel to the horizon.c) The celestial equator passes through the zenith.d) In the course of a year, every stars are visible.e) The sunlight rises top top September 23 and does not set until march 21 (ideally).ANSWERa) Earth"s Equatorb) Earth"s north or south PoleAt the phibìc (geographic) Pole, an observer will only ever have the ability to see the top (Northern) halfof the Celestial Sphere. The observer would certainly never have the ability to see a constellation such together the SouthernCross since it is in the southern half of the Celestial Sphere. In ~ the Earth"s south Pole, an observerwill just ever be able to see the southern half of the Celestial sphere (they would never be may be tosee the big Dipper).c) Earth"s Equator (the Celestial Equator would be straight overhead)d) Earth"s EquatorAll stars deserve to be it was observed at part time during the year from the Earth"s Equator. That course, onlyone-half the the Celestial Sphere deserve to be watched at any kind of given time in ~ any specific point on the Earth. However, end a period of 6 months, the planet is ~ above opposite political parties of the Sun and thus an observeron the equator will check out both (opposite) political parties of the celestial sphere. Therefore an observer in ~ theEquator will see all the constellations (e.g., little Dipper and Southern Cross).
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E) Earth"s southern Pole (note the it is summer in the southern hemisphere)This is why the regions inside the Antarctic one (and Arctic Circle) are described as "The Landof the Midnight Sun" due to the fact that on at the very least one day during the year (number that days depends on Earth"slatitude) there will be at the very least 24 hours of constant daylight. Throughout their particular winters, therewill also be at the very least 24 hours of continuous darkness.