Of course that depends a bit on what we mean by a year and a day.
You can measure the Earth's position relative to the stars or you can count days. If you do this you find a day - a star day (the proper term is sideral from the Latin word for star -- sidus). Do this and you measure about 86,164 seconds ... 23 hours, 56 minutes and 4 seconds ... er ... not 24 hours.
The issue is the Earth moves along its orbit - about a degree per day - as it rotates. It takes a few minutes for the Earth to rotate to the point where the Sun, not the stars, should be to mark a new day.
If you divide the number of seconds it takes the Earth to orbit the Sun, 31,558,149, by the number of seconds in a solar year you get something that isn't 365 -- about 365,256 days. And so there is the leap year.
It turns out that isn't really correct either. The Sun is not a point and the Earth does not orbit relative to the center of the Sun. More important is the fact that our orbit is not circular, but slightly elliptical - the length of a day is constantly changing (check out the equation of time). And the axis of the Earth slowly precesses relative to the stars sweeping out a motion in about 20,000 years. And there is a relativistic correction -- and so on.
But if you ask a physicist a question where accuracy isn't terribly important, she will approximate the year Π * 107 seconds .. accurate to better than a half percent and just fine for back of the envelope work.:-)
You can use the Earth's orbit as the basis of a measurement of distance . No one uses the distance the earth travels, but imagine a huge long right angled triangle where the shortest side is the average distance from the Earth to the Sun (1 astronomical unit or 1 AU). If the angle between the long legs is a second of arc the length of the second longest leg - the leg that would go from the far away point through the center of the Earth's orbit - would be a huge distance ... about 1.92 * 1013 miles. This is called a parsec for the parallax of one arcsecond. It was a popular way to measure the distance to nearby stars, but light years have replaced it - a parsec is about 3.26 light years.
Light in a vacuum travels at a constant speed. It is the speed limit of the Universe and a really handy measure for distances even though it is fast enough that it is difficult for us to imagine the distance light travels in a year. The Moon is about 1.3 light seconds away and the Sun about 500 light seconds distant.
Many operations in computers take place in increments of a billionth of a second (a nanosecond). Light travels about 30 centimeters in a second - close to a foot. A friend is very tall and is constantly asked her height - she sometimes answers "six and two thirds nanoseconds"... I'm about six nanoseconds tall and you can figure out your own lengths. This is a neat scale - it takes a fast speed that our senses can't comprehend and combines it with a time that is also beyond our normal experience and gives us a way to state something that is very everyday.
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