L>aramuseum.org 113Assignment #1SOLUTIONSChapter 117. Mean you space on a weird planet and observe, in ~ night, the the stars carry out not climb and set butcircle parallel to the horizon. Now you go in a constant direction because that 8000 miles, and at her newlocation ~ above the world you find that all stars rise straight up in the east and collection straight under in thewest, perpendicular come the horizon.a) How could you identify the one of the planet without any type of further observations?c) What is the circumference, in miles, of that planet?Since the stars carry out not climb or set, you need to be in ~ the north (or South) pole of the planet. Once youwalk to the allude where the stars climb and set perpendicular to the horizon, you room at the equator ofthe planet. ANSWERa) through walking from the phibìc pole come the equator, you"ve covered 1/4 of the circumference of thesphere (viewed together a circle). Therefore by multiplying by 4, you can determine the entirecircumference.c) since the distance is 8000 miles, the whole circumference that the planet need to be 4 x 8000 miles= 32000 miles.Chapter 214. What is the semimajor axis the a one of diameter 24cm? What is the eccentricity?ANSWERA one of diameter the 24cm has actually a significant axis (from one leaf diametrically throughout to the other edge)of 24cm. The semimajor axis is one-half that the major axis (= 24cm / 2 = 12cm). Together you deserve to see,it is just the radius the the circle and equal to 12cm. A circle has actually an eccentricity the zero.Chapter 219. What would be the duration of a planet whose orbit has a semi-major axis that 4 AU? Of one asteroidwith a semimajor axis that 10 AU? ANSWERAccording come Kepler"s third Law, P2 = D3 where P is express in systems of years and D in systems ofAU. Hence P = D3/2. For a planet that has D = 4 AU, ns = (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 earth according to the following descriptions? (Refer back to chapter 1as well together this chapter.)a) The stars increase and collection perpendicular come the horizon.b) The stars circle the sky parallel to the horizon.c) The celestial equator passes v the zenith.d) In the food of a year, every stars room visible.e) The sunlight rises ~ above September 23 and also does not set until march 21 (ideally).ANSWERa) Earth"s Equatorb) Earth"s north or southern PoleAt the phibìc (geographic) Pole, one observer will only ever be able to see the top (Northern) halfof the Celestial Sphere. The observer would certainly never be able to see a constellation such together the SouthernCross due to the fact that it is in the southern half of the Celestial Sphere. In ~ the Earth"s southern Pole, one observerwill only ever be able to see the southern fifty percent of the Celestial round (they would never ever be maybe tosee the big Dipper).c) Earth"s Equator (the Celestial Equator would certainly be directly overhead)d) Earth"s EquatorAll stars deserve to be observed at part time during the year from the Earth"s Equator. That course, onlyone-half of the Celestial Sphere can be viewed at any given time in ~ any particular point on the Earth. However, end a period of six months, the planet is top top opposite political parties of the Sun and also thus an observeron the equator will watch both (opposite) political parties of the celestial sphere. Thus an observer at theEquator will watch all the constellations (e.g., small Dipper and Southern Cross).

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E) Earth"s southern Pole (note that it is summer in the southern hemisphere)This is why the areas inside the Antarctic one (and Arctic Circle) are referred to as "The Landof the Midnight Sun" because on at least one day throughout the year (number that days relies on Earth"slatitude) there will be at least 24 hours of consistent daylight. During their respective winters, therewill additionally be at the very least 24 hrs of continuous darkness.