As you learned in August, eclipses are scary. [ citation needed ] Suppose you wa

Question

As you learned in August, eclipses are scary.[citation needed] Suppose you wanted to outrun the shadow of this last eclipse; how fast would you have had to move to avoid being overtaken by the shadow? (Note: In 1973, a Concorde prototype was modified with rooftop portholes to allow scientists to extend the length of time they could observe the totality of the eclipse to 74 minutes by taking advantage of the aircraft's capability to travel at very high speeds.)

It turns out that calculating the speed of an eclipse's shadow is pretty mathy and, even after fixing various values for the conditions at the time of the last eclipse, it still depends upon the latitude of the observation point, the angle from the observation point to the tangent line parallel to the moon's orbit, and the elevation of the moon in sky. Assuming NASA got the math right, the specific formula to calculate a reasonable estimate of the shadow speed is:

vs=1.23cos(23)6.61×105(35571674cos(l))dsun(3784751.0025dmoon+6378cos())cos()sin(e)vs=1.23cos(23)6.61×105(35571674cos(l))dsun(3784751.0025dmoon+6378cos())cos()sin(e)

where vsvs is the speed of the shadow in km/h; ll is the latitude of the observation point in degrees; is the angle, in degrees, along the path of totality from McClellanville, SC to the observation point; ee is the elevation, in degrees, of the sun and moon above the horizon at the observation point; and, for the recent eclipse, dsun=151,390,000dsun=151,390,000 and dmoon=372,000dmoon=372,000 [Source: NASA].

Write a function named lunar_shadow_speed() that has parameters for the latitude of the observation point, theta, and sun/moon elevation and RETURNS the velocity of the lunar shadow according to the formula above, rounded to the nearest integer.

Explanation / Answer

I have wrote the program but its not giving correct output.There is probably something wrong in the equation given in question,According to given equation i have written the following program-

import math

def lunar_shadow_speed(latitude,theta,elevation):
dsun=151390000
dmoon=372000
vs=1.23*math.cos(23)*6.61*10-5*(3557-1674*math.cos(latitude))*dsun*(378475-1.0025*dmoon+6378*math.cos(theta))*math.cos(theta)*math.sin(elevation)
return int(round(vs))

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