{"id":6681,"date":"2024-02-29T04:15:07","date_gmt":"2024-02-29T09:15:07","guid":{"rendered":"http:\/\/www.tubridy.net\/newblog\/?p=6681"},"modified":"2024-02-29T06:58:18","modified_gmt":"2024-02-29T11:58:18","slug":"orbits","status":"publish","type":"post","link":"http:\/\/www.tubridy.net\/newblog\/life\/orbits\/","title":{"rendered":"Orbits"},"content":{"rendered":"\n

Happy Leap Day!<\/em><\/strong><\/p>\n\n\n\n

In recent years, I have turned to star gazing. I am particularly fascinated by how the Moon, planets, and stars move through the sky. The Moon, in particular, never seems to be where I think it should be or oriented the way it is!<\/p>\n\n\n\n

Today is a very special, interesting day. For the longest time, I thought that the extra day added every four years was to account for the fact that there are approximately 365 1\/4 days per year. So 4 times 1\/4 is equal to one day. And since it’s not exactly 1\/4 of a day, we skip the extra day every 400 years.<\/p>\n\n\n\n

Sort of….<\/em><\/strong><\/p>\n\n\n\n

It turns out the real story is much more complex and interesting! I recently read an article in Big Think<\/a><\/em> about what a day and year actually mean in terms of Earth’s orbit around the Sun and the influence of the Moon on Earth. It points out how this has changed over the millennia. For example, days last only 6-8 hours during the early days of the earth!<\/p>\n\n\n\n

Rotating While Rotating<\/h2>\n\n\n\n

As the Earth rotates daily, it is more slowly circling the Sun. This introduces a variation when the Sun peaks during the day. The result is that what we perceive as a ‘day’ from the Sun’s position is a little longer<\/strong> than it takes for Earth to complete a complete (360-degree) rotation (23 hours and 56 minutes and 4.09 seconds)<\/p>\n\n\n\n

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To travel once around Earth\u2019s orbit in a path around the Sun is a journey of 940 million kilometers. The extra 3 million kilometers that Earth travels through space per day ensures that rotating by 360 degrees on our axis won\u2019t restore the Sun to the same relative position in the sky from day to day. This is why our day is longer than 23 hours and 56 minutes and 4.09 seconds, which is the time required for the spheroidal Earth to spin a full 360 degrees. Similarly, a \u201cyear\u201d is not the time it takes for Earth to make a complete 360-degree revolution around the Sun but is determined by the return of its axis to the same position relative to the Sun to the year before.<\/figcaption><\/figure>\n\n\n\n

I’ve always found it interesting to think about how ‘fast’ we are going on Mother Earth relative to a fixed point in space. The earth moves at roughly 67,000 mph in its journey around the sun. It seems that Earth’s cruise control doesn’t work very well as we are slightly changing speed during the course of one revolution around the Sun!<\/p>\n\n\n\n

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Before we understood how the law of gravity worked, we were able to establish that any object in orbit around another obeyed Kepler\u2019s second law: it traced out equal areas in equal amounts of time, indicating that it must move more slowly when it\u2019s farther away and more quickly when it\u2019s closer. For extremely elliptical orbits, such as comets, the velocity near perihelion is enormous, while the velocity near aphelion is relatively tiny.<\/figcaption><\/figure>\n\n\n\n

This means that the length of one-day changes and doing so in the most interesting way!<\/p>\n\n\n\n

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This graph shows the equation of time for a specific location on Earth. Where the slope of the graph is positive, days are shortening; where the slope is negative, days are lengthening; where the slope is zero (at the four locations marked), the day is precisely 24 hours. This happens four times per year in a latitude-dependent fashion.<\/figcaption><\/figure>\n\n\n\n

This is another very cool example of complex sinusoidal motion and waveforms. Fascinating!<\/p>\n\n\n\n

What Exactly is a Year Anyway?<\/h2>\n\n\n\n

The next cool fact is a little hard to grasp at first. I’ve always known that the Earth’s rotation axis is tilted (23.5 degrees), but it turns out the axis precesses over time (20,000 years). <\/p>\n\n\n

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Think of a spinning top where you see the very top wobble to trace a circular path. <\/em><\/p>\n\n\n\n

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The Earth, moving in its orbit around the Sun and spinning on its axis, always defines \u201cnoon\u201d and \u201cmidnight\u201d in the same fashion: where the Sun\u2019s height above or below the horizon is maximized. This moment in time doesn\u2019t correspond to when Earth has rotated 360 degrees from the prior day, but rather closer to 360.9856 degrees, owing to the added effects of Earth\u2019s motion around the Sun.<\/figcaption><\/figure>\n\n\n\n

The net effect is that every time the Earth completes a full rotation around the Sun, it is positioned slightly differently than the previous rotation. The time it takes for four complete seasons (for example, the time between summer solstices) is 20 minutes shorter than for one full rotation around the Sun.<\/p>\n\n\n\n

Long, Slow Burn<\/h2>\n\n\n\n

Finally, it makes sense to me that everything is slowing down. It’s sort of like increasing entropy. I was surprised to learn that over the course of Earth’s history, it has slowed from 6 to 8 hours a day to 23 hours, 56 minutes, and 4.09 seconds.<\/p>\n\n\n\n

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The Moon exerts a tidal force on the Earth, which not only causes our tides but also causes braking of the Earth\u2019s rotation and a subsequent lengthening of the day. The asymmetrical nature of Earth, compounded by the effects of the Moon\u2019s and Sun\u2019s gravitational pulls, causes the Earth to spin more slowly. To compensate and conserve angular momentum, the Moon must spiral outward. For this reason, Earth will no longer have total solar eclipses after another 600 million years, and the length of each day will get longer as time progresses.<\/figcaption><\/figure>\n\n\n\n

If we keep using our current calendar, we will eventually not need a leap day and will even have to eventually remove a day from the calendar rather than add one.<\/p>\n\n\n\n

Just How Fast Are We Going, Anyway?<\/h2>\n\n\n\n

One other cool fact. While traveling at 67,000 mph around the Sun, the Sun is rotating with a fantastic velocity of 448,000 mph around the galactic center (a big black hole called Sagittarius*). The Milky Way itself is moving 1,300,000 mph through the Universe.<\/p>\n\n\n\n

What Does This All Mean?<\/h2>\n\n\n\n

Check it out!<\/p>\n\n\n\n

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