How to Prove 367 Days for Leap Year?

Hello Guys,

Welcome to Rusty Science. This is not a fishy title. Please read till end of the post to understand how leap year can have 367 days.

What is a Day?

To understand a year it’s very essential to know what a day is. Obviously you may know, because all our childhood text book says that it’s a time taken for earth to take complete 360 degree rotation. Is it true? That’s where the problem starts. When we say complete 360 degree rotation, you may need to answer the question with respect to the what? Because earth can play some sort of a dirty trick and say that "hey! I have completed 360 degree rotation". To avoid this issue I want to give one of a metaphoric solution. If you are driving in a car in a highway or something, the objects closer to you will move faster but object far from you will not move that much fast. It will be too slow and it is very difficult to distinguish that it is moving. That’s the principle we are going to follow to find earths 360* rotation.

Sidereal Day:

Since distant objects move slower, we can take a distant star (far far away star) as a reference point in order to find out whether our earth has taken 360 degree rotation. You may ask how this can help?. Whenever the distant star appears above your head, that we can take as a reference time and whenever the next time the same star comes above your head then you can say earth has actually taken 360 degree rotation. So we can consider that as one day. 

That solves our problem right? No.

Whenever earth takes a complete 360* rotation with respect to a distant star that is called Sidereal Day. But Sidereal Day will not have 24 hours. It will have slightly lesser than 24 hours. We can say that as 23.9 hours (23 hours 56 minutes and 4.1 seconds).  But what we taught is, a day will have 24 hours. How did we come to that conclusion then?

Solar Day:

Our important events like day/night or seasons; all those things are not depends upon the distant star but a very close star of ours "SUN". So we should consult with sun in order to find out whether it’s a day or not.

But the problem is. Distant star and earth has a difference. That is, we are not revolving around distant start but we are revolving around sun. Take this example, if we see from above (north pole), earth will look like it is spinning in counter clock wise direction and in the same way, earth will take a circle around sun in counter clockwise direction. 

In that case, once 360 degree rotation is done, with respect to the distant star one day (sidereal day) is done with respect to distant star. Yet it requires some extra turn in order to face towards the sun. We will only consider when the particular reference star comes above our head. Since we are consulting sun for finalizing day, sun needs to come above your hear in order to say that one day is complete. But sun will come above your head once the little movement (we can consider it as theta) is added. 

In that case 23.9 hours taken to one 360 degree rotation, but this extra theta (0.1 Hour or ~1 degree) is taken for earth to re-position itself to the sun. 

This theta is variable across the year.

Example.

In space-time fabric. consider that earth is not at all gonna spin. In that case, When the earth comes around the sun, always one point is facing towards sun (as same as moon facing towards us). Everyday one side of the earth will have morning (ex. Africa), other side will have night. it will never change throughout the year. 

In the picture there are 4 earths mentioned, but in all the 4 earths, Africa is facing towards sun. If you consider distant star exist somewhere in the far left corner, with respect the that distant star earth 2 (Top earth in picture) already drifter by 90* (With respect to right hand side earth). If we continue moving in counter clockwise direction, each position earth is drifter by 90* from it's previous position with respect to distant star. Though earth did't move with respect to Sun (not even a single day), with respect to distant star we have already took (4 x 90*) 360* rotation, that is a complete one rotation. If we take one complete rotation with respect to distant star, we call it sidereal day. So if earth is not at all moving, still there will be one sidereal day for every year. This one complete rotation will not be noticed if you are staying inside earth, but if you are staying in the distant star you can see it. This 360 degree rotation is used by earth to re-position itself to the sun.

Summary:

366 days for leap year right. So you can find that there is one extra 360 degree rotation been taken with respect to the distant star every year (that is not with respect to sun). This extra 360 degree rotation is to re-position earth to face sun. When I say 367 days for leap year I did not mean that it’s with respect to sun which is called solar day, I meant with respect to the distant star which is called Sidereal Day. So, I want to clarify that we do have 367 days for every leap year but not solar days, it’s Sidereal Days. Hope you understand what Sidereal Day is and what a solar day is. If you didn’t understand, we have our YouTube channel called "Rusty Science". I have explained everything with demo station. Please feel free to visit. Click here to view it. If you have any question regarding this post, comment below I'll answer it.
Thank You.

Rusty Leo

References:
Image and Content Courtesy: Vsauce
Links: http://astronomy.swin.edu.au/cosmos/S/Sidereal+Day
https://en.wikipedia.org/wiki/Sidereal_time
https://www.youtube.com/watch?v=IJhgZBn-LHg
https://youtu.be/cvcSd86bQBA

Free Resources:
I have downloaded a book with amazing earth's photography from NASA site. If you think it will be useful to you, Please download that book here.

Watch the video here: