What day/night cycle would we have if earth was tilted like Uranus?
Uranus is nearly rolling about its fixed spin axis, One pole faces and the other is hidden, alternately, through half orbital periods of 42 years. This half will be 6-month period, for the Earth.
I've revised my response to address the legitimate question posed by M. Zack. Uranus has an orbital period of 84 years and a spin period of 0.718 Earth days. To put it succinctly, the planet takes 42 years to transition from day to night. Its spin axis is inclined at an angle of approximately 0.8 degrees to its orbital plane, and the equatorial plane is almost perpendicular to it. For Earth, this means that half of the transition will occur every six months. A useful resource for clarification (apart from Zack's question) is cseligman.com/planets/uranusrot.htm.
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The day/night cycle would be very different if Earth were tilted like Uranus, which has an extreme axial tilt of about 98 degrees. Rather than having 24-hour day/night cycles as we do now, there would be long periods of continuous daylight and darkness at different latitudes, depending on the time of year; around 42 years of continuous daylight and 42 years of continuous darkness at the poles; more regular day/night cycles at the equator, but with much variation in the length of each cycle throughout the year.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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