Reference no: EM13147427
Q.1Finally, we will look at a system that is in an orbit comparable to the Earth to see how the angle that the light strikes the surface and the length of day contribute to the total amount of energy that we receive from the Sun at the two solstices. Recall that the changing distance of the Earth gives a maximum difference of about 6% between the closest and farthest distances. We will find that the effects studied here are much larger than this.
Before continuing we need a little more information about the angle factor given in the formula above. It turns out that the angle factor is equal to the cosine of the angle that the light strikes the surface as measured from perpendicular. In this question, the angle factor will be calculated for you. However, it is still informative to see how that factor is calculated for an observer at a given latitude and with a given tilt of the planet.
Set the tilt of the planet to be 20 degrees.
a) What is the length of day during the winter solstice for this planet?
b) What is the length of day during the summer solstice for this planet?
c) The angle factor for the winter solstice is cos(45 + 20) = 0.423. What is the total amount of sunlight-hours on the winter solstice for this planet? (Be sure to show your work on all of the following questions.)
d) For the summer solstice the angle factor is equal to cos(45 - 20) = 0.906. What is the total amount of sunlight-hours for the summer solstice?
e) What is the ratio of the sunlight-hours for the summer solstice to the winter solstice (divide the larger number by the smaller). You should get an answer that is larger than 1.06 (the ratio due to the changing planet-Sun distance).
Q.2Now, wait until the planet is at the winter solstice (12:00am). a) How many hours of daylight are there on the winter solstice with the inclination at 45 degrees? Use the same criteria for the length of day that you used for the previous question.
b) Use the above formula and the results from the earlier questions to calculate the number of sunlight-hours of daylight that one receives on the winter solstice for a planet tilted by 45 degrees. Show your work for full credit.
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