Saturday, August 25, 2012

Q: If one day is not exactly 24 hours and is in fact 23 hours, 56 minutes, shouldn't the error add up, and shouldn't we see 12 a.m. becoming noon?

You're right that a "sidereal" day is about 23 hours, 56 minutes, 4 seconds. But this is not a day in the everyday sense.

A sidereal day is how long it takes the earth (on average) to make one rotation relative to the faraway stars and other galaxies in the sky.

If you find a star that is directly above you at midnight one night, the same star will be directly above you again at 11:56:04 p.m. the next evening.

Similarly, if you were sitting on the star Proxima Centauri looking through a powerful telescope at earth, you would see Toledo, Ohio, go by every 23 hours, 56 minutes, and 4 seconds.

However, we don't keep time by the faraway stars -- we measure time by a much closer star, the sun! And we are actually in orbit around the sun, orbiting in the same direction that the earth is spinning on its own axis. From our perspective, the sun goes a little slower in the sky because we are also orbiting around it.

How fast are we orbiting around the sun? We make one full orbit every year, or roughly 366.25 sidereal days.

So after a year, the faraway stars will have done 366.25 rotations around the earth, but the sun will only have done 365.25 rotations. We "lose" a sunset because of the complete orbit. (The extra quarter day is why we need a leap year every four years.)

So there are 365.25 "mean solar days" in 366.25 "sidereal" days. How long is a "mean solar day"? Let's do the math: One sidereal day is 23 hours, 56 minutes, 4 seconds, or 86164 seconds. Multiply this by 366.25 sidereal days in a year, and you get 31557565 seconds. Divide by 365.25 solar days, and we get that a solar day is.... 86,400 seconds. That's 24 hours exactly!

It's this "mean solar day" (24 hours) that is the normal definition of day.

If you want to do the math more exactly, a sidereal day is 86164.09054 seconds, and a tropical year is 366.242198781 sidereal days. That works out very closely.

(P.S. Unfortunately, the earth's spin has been slowing down because the moon is sucking away the earth's energy. Every time the high tide of the Atlantic Ocean slams into the east coast of North America, the earth slows its spin a little bit. The definition of the second is based on the speed the earth was spinning back in 1820, and we have slowed down since then. As a result, we occasionally have to add in a "leap" second to the world's clocks. See http://online.wsj.com/article_email/SB112258962467199210-lMyQjAxMTEyMjIyNTUyODU5Wj.html?mod=wsj_valetleft_email)

27 comments:

  1. So after a year, the faraway stars will have done 366.25 rotations around the earth, but the sun will only have done 365.25 rotations.

    Isn't that a wrong statement.

    Shouldn't that be: "So after a year, the earth will have done 366.25 rotations around the faraway stars, but will only have done 365.25 rotations around the sun."

    ReplyDelete
    Replies
    1. No, because we can take the Earth as the centre of the universe (relatively speaking). Since historically (but also PRACTICALLY today!) we observe motion relative to our own frame of reference, the centre of which is the Earth, not the sun or a star. (Obviously we rotate around the sun and with the sun around a galactic centre, but from our perspective we are at the centre)

      Hence the stars appear to rotate around the Earth, just like the sun apears to rotate around the Earth. Just like the rails and the trees appear to move when you are on the train and everything on the train with you appears to be still.

      Hence the difference between a sideral and a solar day: one is based on the RELATIVE motion of the "fixed stars" around the Earth and the other the relative motion of the sun.

      (btw the stars are caled "fixed", because they appear not to move at all... since they are so far away. Hence before modern technology it was very difficult to detect any motion of the stars, since a perceptible change in the position of the stars might be detected only between quite long time spans, centuries or millennia even.)

      Delete
    2. Actually,the sun moves away from the center of the universe. As it moves,the planets "try to escape the gravitational pull from our star" . There is "drag and push " energies. Also the moon doesn't "spin"around the earth. As the earth "travels" around the sun,the moon "weaves" a path,around earth,around the sun and rotates so the same side faces earth. Quite a statement for there being a GOD! No man could do this.

      Delete
  2. NO! That isn't correct either. Relative to other stars the Sun is (sort of) fixed. Because of the Earth's rotation around the Sun, the other stars APPEAR to rotate around the Earth. In fact, they don't. And the Earth would have to travel an incredible distance to rotate around a faraway star.
    The Sun's position to a faraway star is not really fixed - everything is in motion - but it does not play in this discussion.

    ReplyDelete
  3. There Are Actually 365.25 & There Are 24 & Almost 1 Extra Minute

    ReplyDelete
  4. ALL OF YOU ARE WRONG. WE ACTUALLY HAVE 26 HOURS A DAY, 13 HOUR CLOCK, BECAUSE THERE IS SMALL ISLANDS THAT NOT A LOT OF PEOPLE LIVE THERE, THERE IS UTC+13 AND 14, SO WE HAVE ADDITONAL 2 HOURS, BUT WE JUST NORMALLY DON'T COUNT THE ISLANDS, SO WE JUST SAY 24 HOURS IN A DAY. SCREW YOUR SELF NOW, I'M DONE FOR NOW, BUT WILL BE BACK, I HOPE, I GUESS, BYE NOW.

    ReplyDelete
  5. ALL OF YOU ARE WRONG. WE ACTUALLY HAVE 26 HOURS A DAY, 13 HOUR CLOCK, BECAUSE THERE IS SMALL ISLANDS THAT NOT A LOT OF PEOPLE LIVE THERE, THERE IS UTC+13 AND 14, SO WE HAVE ADDITONAL 2 HOURS, BUT WE JUST NORMALLY DON'T COUNT THE ISLANDS, SO WE JUST SAY 24 HOURS IN A DAY. SCREW YOUR SELF NOW, I'M DONE FOR NOW, BUT WILL BE BACK, I HOPE, I GUESS, BYE NOW.

    ReplyDelete
  6. I'm pretty sure there are 24.3 hours in a day,making 365.25 days in a year.The .25 adds up to one day known as the leap day every 4 years.However it doesn't add up to a full day,WHICH IS 24.3 HOURS.

    ReplyDelete
    Replies
    1. Wow, your stupidity is truly impressive...

      Delete
  7. Just put the fucking number. You don't have to write an entire article about it fuckhead.

    ReplyDelete
    Replies
    1. Wow! Your command of civilised speech is truly UNimpressive. Best that you keep the vulgar stuff for just you and your mates.

      Delete
  8. I thought the hours in a day were just however a person wants his or her clock calibrated ,time a night on a power pole from sunrise to sunrise and have a clock computer programmer divide that into how many hours minutes and seconds you want , a digital watch is just a computer program basically. anything a person wants ,

    ReplyDelete
  9. This comment has been removed by the author.

    ReplyDelete
  10. This entire model is wrong and very easy to prove so. If it is noon on Jan 1 and the sun is directly overhead, i.e. you are facing the sun, and as we have concluded, except for brainiac above who thinks there are 26 hours in a day, the rest of us know there are basically 24hrs in a day. We can also say this model of the sun and the earth makes 1 full complete 360 degree rotation in that 24 hours. Now fast forward 180 days to about July. It is now noon again, and you have made exactly 180, full 360 degree turns. You are also exactly 180 degrees from where you started on January 1. Problem is you are facing 180 degrees opposited the sun in complete darkness with the sun on the opposite side of the earth, yet it is still noon. It doesn't work no matter what you do to try and make it so. It's a little fact they have always hidden in plain sight. Now, ask your self why your education programs, your teachers, and your governments have lied to you and told you the the earth is a round ball that circles around a sun your entire life. Simply it can not be.

    ReplyDelete
    Replies
    1. I just randomly had this thought earlier in the evening and my friends couldn't grasp what I was tryig to explain to them. It seems like such a stupid thing to try to cover up, but at the same time seems impossible for me to try to prove false. Can't find anything on the subject!

      Delete
    2. A full orbit around the sun (a year) is not 360 days. A non-leap year has 365 days. The earth rotates another two and a half times on its axis by the time it completes a full 180° around the sun.

      Delete
    3. Shaun, I have been pondering this same thing. And wondering Why if the true day is 23hr 56 minutes but we have a 24 hour clock, then in one year of 365 days we will have 1,460 minutes or 24.3 hours of time Ahead of where 365 rotations Should be. So that is one thing.

      The other is, with that in mind from a ball earth POV. I thought, if we keep the same facing point/direction for our full rotation. I know the thing about compasses but just work with me on this for a moment, ok... in 23hr 56 minutes the ball Earth will have made one rotation from N facing to N facing. We agree on this (I am using N only as a directional marker and not an actual direction, it could just as easily be 12 oclock on a clock face for this purpose). BUT, from Ball Earth POV, it will also now be slightly to the Side of the Sun, which was also originally N of our starting point but is now ever so slightly NW now compared to the start point. With the 24 hour clock we don't consider the rotation to be complete for another 4 minutes. In that time BE will have Spun just a small amount more and so while the True full rotation was 360 deg in 23 hrs 56 min, our 24 rotation is 360 + a bit. And with that extra Bit we now still face the Sun.

      I already showed that with the extra 4 minutes there is an entire day ahead of ourselves. But over 6 months that is 12 hours ahead of actual. That places us on the opposite side of the Sun to which we started in BE model, the True rotation starting face is facing Away from the Sun as you know and said, but we, with our 4 extra minutes are a full 12 hours out of sync with that and are facing in the opp direction, or To the Sun.

      In other words, after 6 months of BE rotations, the point which did face the Sun is now on the opp side of the Sun and facing away from the Sun. YOu are correct. BUT, because we added 4 minutes every day, and we go by that man made clock time, in 6 months time our man made clock has us a full 12 hours out of sync and thus we are in daylight instead of darkness, as it would be if we had used a 23.56 clock time.

      IN terms of clock minutes... actual 23.56 rotation is 1436 minutes in a day while we work on 1,440. After 182 days (or 182.5 for a 365 day year) the Earth 23.56 clock has done 182 spins for 261,352 minutes or 4,356 hours. The 24 hour clock will be 262,080 minutes or 4368 hours. The difference between the two is 12 hours. So we are 12 hours out of sync and facing 180 deg in the opp direction, and thus To the Sun.

      Does that makes sense?

      This still doesn't prove BE, but explains why we aren't facing away from the Sun after 6 months.

      Delete
  11. hello thank you for the info

    ReplyDelete
    Replies
    1. You are welcome. And for those that want to conclude that there are "really only 23 hr 56 min in a day" and you run the math and 4 min x 180 days = 720 min, then 720 min ÷ 60 min/hr = 12 hr which flis what side the earth you are on" well you need to then show me that every clock in the world is set to roll over at 23 hr 56 min., because as far as I know, every clock I own, and every clock I have seen has 24 hour exactly for every day, and I don't set my clock back 4 min every day, or 12 hours every 6 months because I find that when I went out at noon to water the garden, it was actually pitch black because the sun was on the wron side if a globe model earth. It is sheer nonsensical, and only works mathematically and not by emperical ovservation. Use your eyes and your brains. The globe model doesn't work. Try to debunk this. Hiding the truth is the greatest evil. I tried to debunk, and now this is why i now know the truth. https://youtu.be/7OLxiWFquus

      Delete
    2. Please prove me wrong and I will retract my comments.

      Delete
    3. This comment has been removed by the author.

      Delete
    4. ShaunTheSheep, think about it another way. Using a sidereal day (23h 56m 4s) instead of the current definition of 24 hour day would be great for astronomers. Why? Imagine that every night in January you go out on your south-facing deck at 11pm and look up and see the star Sirius. If we were using a sidereal day (1 exact rotation of the earth = 24 hours) everyday at 11pm you would be able to see Sirius in the exact same place in the sky. Fast forward to July. Since you are using a sidereal day, 11pm is daytime in July. You go out on your south-facing deck at 11pm and point to the exact spot where Sirius is. You know it's there. You can't actually see Sirius because the sun is out, but you know that it's there because on sidereal time the earth is always in the exact same place at 11pm relative to the stars. With using a 24 hour day as defined by what is practical for normal life, the stars move each night by four minutes so that the sun is high in the sky (i.e. crosses the meridian) at noon year-round. I don't think the scientific community would mind switching to 24 hours = Sidereal Day, but for normal people they like it being daytime at noon year-round.

      Delete
  12. Lol your using a clock that is set at 23h56min to roll they achieve this by playing with how long a second is.other why's you'd have to do daylight saving time alot.

    ReplyDelete
  13. Sorry also in old days before your watch was a computer.everyone set there watches at high noon everyday. High noon being when sun is straight up.this isn't practical in today's world work times school so forth.I hope this helps

    ReplyDelete
  14. Jordan K, what you are missing is simple. It takes 23h 56m 4s for the earth to spin 1 full rotation (a sidereal day). Since we are going around the sun it takes roughly 4 mintues longer each day (24 hours) for the sun to be roughly at the meridian at noon from day to day. Having a 24 hour day based on the sun is much more practical than using a sidereal day. If we used a sidereal day 1pm would be daylight in summer and night in winter (or vice versa). So the earth spins 366.25 full spins each year, but we only see the sun rise and set 365.25 times. Our 24 hour day is based on seeing the sun cross the meridian at roughly noon standard time each day--which is more than 1 rotation per day (~4 minutes more).

    ReplyDelete