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Sunrise time

Suppose the earth has no inclination on its orbit. It orbits the sun in a perfectly circular path. You are located exactly on the equator and at UTC +0000. Thus sunrise occurs everyday exactly at 6 am. Ignore atmospheric refraction and size of the solar disc. A solar day on earth is exactly 24 hours and a solar year is exactly 365 days.

a)If you change your latitude, how does the time of sunrise change? What will be the time of sunrise at 25° latitude?

b)If the earth did not orbit the sun in a perfect circle, how would the time of sunrise change? What would be the time of sunrise at perihelion with 0.1 eccentricity?

c)If the earth had an axial tilt, how would the time of sunrise change? What would be the time of sunrise on vernal equinox, autumnal equinox, summer solstice, winter solstice with an axial tilt of 25°? How will the time of sunrise change a day after/before vernal equinox/summer solstice?

d)How do GMT and LST of sunrise change with longitude?

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