Let's call the angular velocity with which the Earth rotates around its axis omega and the average angular velocity with which it rotates around the Sun, alpha. Then the average angular velocity at which the Sun moves in the sky is omega - alpha and this is equal to 2 pi/day. So, we have
omega - 2 pi/year = 2 pi/day -->
omega = 2pi/day - 2 pi/year (1)
omega stays the constant due to conservation of angular momentum of the Earth w.r.t. its center of mass. Due to the Eart's eliptical orbit, alpha does not stay constant, 2 pi/year is just the average over an entire year. We ahve:
2pi/day = omega + alpha
whhere you compute omega from (1). This allows you to solve for the length of a day if you know alpha. Now, alpha can be computed from conservation of angular momentum of the Earth w.r.t to the Sun. We have that:
alpha r^2 = constant, so if the distance to the Sun increases then alpha decreases.
Estimate the time difference between the longest day and the shortest day of a year in seconds if you lived on the Earth's equator with the assumptions below.
Note: this is not the difference between solstices as we are adjusting the earth's rotation axis to be in the orbital plane.
Details and assumptions
The furthest distance from the Sun to Earth is df=1.521×108 km.
The shortest distance from the Sun to Earth is ds=1.47×108 km.
To simplify the problem, assume that the Earth's axis is always perpendicular to the plane of its trajectory around the Sun.
The Sun always shines on half of the Earth.
There are 24 hours in a day and 365.25 days in a year.
3 answers
Dude Can`t Understand Please Help
Try 16.13 seconds. Is it correct?