Another orbit? Why, you don't look a rotation older than 4.56 billion years!

By Phil Plait | January 1, 2012 5:59 am

In what is becoming an annual January tradition celebrating my laziness, I’m reposting this article about why astronomers are no fun at New Year’s parties. Well, they can be, but only until you actually say "Happy New Year!" to them, whereupon they’ll corner and lecture you about how to measure orbital periods. It’s amazing any astronomers reproduce. Anyway, here’s the article, which was a lot of fun to originally write, and even more fun to cut and paste here.]


Yay! It’s a new year!

But what does that mean, exactly?

The year, of course, is the time it takes for the Earth to orbit the Sun, right? Well, not exactly. It depends on what you mean by "year", and how you measure it. This takes a wee bit of explaining, so while the antacid is dissolving in your stomach to remedy last night’s excesses, sit back and let me tell you the tale of the year.

First, I will ignore a few things. For example, time zones. These were invented by a sadistic watchmaker, who only wanted to keep people in thrall of his devious plans. So for now, let’s just ignore them, and assume that for these purposes you spend a whole year (whatever length of time that turns out to be) planted in one spot.

However, I will not ignore the rotation of the Earth. That turns (haha) out to be important.

Let’s take a look at the Earth from a distance. From our imaginary point in space, we look down and see the Earth and the Sun. The Earth is moving, orbiting the Sun. Of course it is, you think to yourself. But how do you measure that? For something to be moving, it has to be moving relative to something else. What can we use as a yardstick against which to measure the Earth’s motion?

Well, we might notice as we float in space that we are surrounded by zillions of pretty stars. We can use them! So we mark the position of the Earth and Sun using the stars as benchmarks, and then watch and wait. Some time later, the Earth has moved in a big circle and is back to where it started in reference to those stars. That’s called a "sidereal year" (sidus is the Latin word for star). How long did that take?

Let’s say we used a stopwatch to measure the elapsed time. We’ll see that it took the Earth 31,558,149 seconds (some people like to approximate that as pi x 10 million (31,415,926) seconds, which is an easy way to be pretty close). But how many days is that?

Well, that’s a second complication. A "day" is how long it takes the Earth to rotate once, but we’re back to that measurement problem again. But hey, we used the stars once, let’s do it again! You stand on the Earth, and define a day as the time it takes for a star to go from directly overhead to directly overhead again: a sidereal day. That takes 23 hours 56 minutes 4 seconds = 86,164 seconds. But wait a second (a sidereal second?) — why isn’t that exactly equal to 24 hours?

I was afraid you’d ask that — but this turns out to be important.

It’s because the 24 hour day is based on the motion of the Sun in the sky, and not the stars. During the course of that almost-but-not-quite 24 hours, the Earth was busily orbiting the Sun, so it moved a little bit of the way around its orbit (about a degree). If you measure the time it takes the Sun to go around the sky once — a solar day — that takes 24 hours, or 86,400 seconds. It’s longer than a sidereal day because the Earth has moved a bit around the Sun during that day, and it takes a few extra minutes for the Earth to spin a little bit more to "catch up" to the Sun’s position in the sky.

Here is a diagram from Nick Strobel’s fine site Astronomy Notes that will help explain this:

See how the Earth has to spin a little bit longer to get the Sun in the same part of the sky? That extra 4 minutes (really 3 m 56 s) is the difference between a solar and sidereal day.

OK, so we have a year of 31,558,149 seconds. If we divide that by 86,164 seconds/day we get 366.256 days per year.

Wait, that doesn’t sound right. You’ve always read it’s 365.25 days per year, right? But that first number, 366.256, is a year in sidereal days. In solar days, you divide the seconds in a year by 86,400 to get 365.256 days.

Phew! That number sounds right. But really, both numbers are right. It just depends on what unit you use. It’s like saying something is 1 inch long, and it’s also 2.54 centimeters long. Both are correct.

Having said all that, I have to admit that the 365.25 number this is not really correct. It’s a cheat. That’s really using a mean or average solar day. The Sun is not a point source, it’s a disk, so you have to measure a solar day using the center of the Sun, correcting for the differences in Earth’s motion as it orbits the Sun (because it’s not really a circle, it’s an ellipse) and and and. In the end, the solar day is really just an average version of the day, because the actual length of the day changes every, um, day.

Confused yet? Yeah, me too. It’s hard to keep all this straight. But back to the year: that year we measured was a sidereal year. It turns out that’s not the only way to measure a year.

You could, for example, measure it from the exact moment of the vernal equinox in one year to the next. That’s called a tropical year. But why the heck would you want to use that? Ah, because of an interesting problem! Here’s a hint:

The Earth precesses! That means as it spins, it wobbles very slightly, like a top does as it slows down. The Earth’s wobble means the direction the Earth’s axis points in the sky changes over time. It makes a big circle, taking over 20,000 years to complete one wobble. Right now, the Earth’s axis points pretty close to the star Polaris, but in a few hundred years it’ll be noticeably off from Polaris.

Remember too, that our seasons depend on the Earth’s tilt. Because of this slow wobble, the tropical year (from season to season) does not precisely match the sidereal year (using stars). The tropical year is a wee bit shorter, 21 minutes or so. If we don’t account for this, then every year the seasons come 21 minutes earlier. Eventually we’ll have winter in August, and summer in December! That’s fine if you’re in Australia, but in the northern hemisphere this would cause, panic, rioting, bloggers blaming each other, etc.

So how do you account for it? Easy: you adopt the tropical year as your standard year. Done! You have to pick some way to measure a year, so why not the one that keeps the seasons more or less where they are now? This means that the apparent times of the rising and setting of stars changes over time, but really, astronomers are the only ones who care about that, and they’re a smart bunch. They know how to compensate.

Okay, so where were we? Oh yeah– our standard year (also called a Gregorian year) is the tropical year, and it’s made up of 365.24 mean solar days, each of which is 86,400 seconds long, pretty much just as you’ve always been taught. And this way, the vernal equinox always happens on or around March 21 every year.

But there are other "years", too. The Earth orbits the Sun in an ellipse, remember. When it’s closest to the Sun we call that perihelion. If you measure the year from perihelion to perihelion (an anomalistic year) you get yet a different number! That’s because the orientation of the Earth’s orbital ellipse changes due to the tugs of gravity from the other planets. It takes about 100,000 years for the ellipse to rotate once relative to the stars! Also, it’s not a smooth effect, since the positions of the planets change, sometimes tugging on us harder, sometimes not as hard. The average length of the anomalistic year is 365.26 days, or 31,558,432 seconds. What is that in sidereal days, you may ask? The answer is: I don’t really care. Do the math yourself.

Let’s see, what else? Well, there’s a pile of years based on the Moon, too, and the Sun’s position relative to it. There are ideal years, using pure math with simplified inputs (like a massless planet with no other planets in the solar system prodding it). There’s also the Julian year, which is a defined year of 365.25 days (those would be the 86,400 seconds-long solar days). Astronomers actually use this because it makes it easier to calculate the times between two events separated by many years. I used them in my PhD research because I was watching an object fade away over several years, and it made life a lot easier.

So there you go. As usual, astronomers have taken a simple concept like "years" and turned it into a horrifying nightmare of nerdy details. But really, it’s not like we made all this stuff up. The fault literally lies in the stars, and not ourselves.

Now if you’re still curious about all this even after reading my lengthy oratory, and you want to know more about some of these less well-known years, then check out Wikipedia. They have lots of info, but curiously I found it rather incomplete. I may submit something to them as an update (like how many seconds are in each kind of year; they only list how many days, which is useful but could be better).

I have to add one more bit of geekiness. While researching this entry, I learned a new word! It’s nychthemeron, which is the complete cycle of day and night. You and I, in general, would call this a "day". Personally, if someone dropped that word into casual conversation, I’d beat them with my orrery and astrolabe.

Incidentally, after all this talk of durations and lengths, you might be curious to know just when the Earth reaches perihelion, or when the exact moment of the vernal equinox occurs. If you do, check out the U.S. Naval Observatory website. They have tons of gory details about this stuff.

Hmmmm, anything else? (counting on fingers) Years, days, seconds, yeah, got those. Nychthemeron, yeah, Gregorian, tropical, anomalistic… oh wait! I know something I forgot to say:

Happy New Year!

CATEGORIZED UNDER: Astronomy, Cool stuff, Geekery, Humor

Comments (46)

  1. SL

    Ohh… My head hurts!

    Happy new… something… :)

  2. Hannu Siivonen

    You could’ve dropped a word or two on where in space a year starts and why – or is that too little math and too much politics for you?

  3. :-D HAPPY NEW YEAR :-D

    To the BA and y’all here hope 2012 is a great one for y’all and for astronomy and science generally. Raises beer and welcomes you to a year that I’ve had the first day of already in my Aussie timezone. :-)

    Starting, of course, with the twin GRAIL spaceprobes entering lunar orbit about now~ish.:-)
    (Click on my name for link on that mission via space-dot-com.)

    Great way to get 2012 off to a flying start and showing even NASA boffins love their moonshine at this time of year. ;-)

    The average length of the anomalistic year is 365.26 days, or 31,558,432 seconds. What is that in sidereal days, you may ask? The answer is: I don’t really care. Do the math yourself.

    Unfortunately I’m lousy at maths. Wish I weren’t & respect those who are good at that but mathematics is a really weak area for me, alas. :-(

    So, umm, has anybody actually done the math on that?

    Now if you’re still curious about all this even after reading my lengthy oratory, and you want to know more about some of these less well-known years, then check out Wikipedia. They have lots of info, but curiously I found it rather incomplete. I may submit something to them as an update (like how many seconds are in each kind of year; they only list how many days, which is useful but could be better). (Emphasis added.)

    Did you ever do that wikipedia update you mention there BA?

    PS. Is using BA for you okay or would you prefer I call you Phil or Dr Plait or something else? Been doing so for a long time here and still not quite sure. I keep meaning to ask.

  4. Tim Gaede

    I like 10^7½ more than π ×10^7. It is more accurate and in my opinion, easier to remember.

  5. Messier Tidy Upper

    Well the first of the GRAIL craft has successfully entered lunar orbit! Congratulations to the GRAIL scientists. Lifts beer in celebration for Gravity Recovery And Interior Laboratory-A’s success. :-)

    For latest GRAIL news see :

    http://www.nasa.gov/mission_pages/grail/news/grail20111231.html

    &

    http://www.nasa.gov/mission_pages/grail/main/index.html

    Whilst the GRAIL wikipedia page can be found here :

    http://en.wikipedia.org/wiki/Gravity_Recovery_and_Interior_Laboratory

    Hope this is interesting / useful for y’all.

  6. Personally, if someone dropped that word into casual conversation, I’d beat them with my orrery and astrolabe.

    Good grief, use a stick or something mundane, not your orrery and astrolabe. And you call yourself an astronomer.

    I liked the Saturday Dilbert cartoon (link in my name, I hope) where someone wishes him Happy New Year and he responds, “I don’t celebrate the magical thinking that one random point in the space-time continuum is somehow special”.

  7. Messier Tidy Upper

    @ ^ Daniel J. Andrews : Magically special no – symbolic and an excuse to get drunk, celebrate an arbitrary time point with friends and family and time off (for most if not all folks) – yes. :-)

  8. Ahmed

    Informative and amusing read as always, Phil. Thanks!

  9. Ed Eastridge

    And people laugh at wibbly wobbly timey wimey stuff. If this doesn’t define that exactly, nothing does.

  10. Alan(UK)

    I am not an astronomer, nor do I play one on television. I have a question for which I have never received a satisfactory answer.

    From ancient times it was generally assumed that the Earth was stationary and everything else revolved around it. Also, from ancient times, people had been tracking the motion of the Sun, stars, and planets.

    Copernicus showed that the existing data could reasonably be explained just as well with an Earth that rotated on its axis and revolved around the Sun.

    Kepler, with the advantage of much more accurate measurements, showed that Copernicus’s hypothesis could be much more concisely explained if the orbits of the planets were elliptical. His results were purely geometric, he offered no physical explanation.

    Galileo, with the advantage of a telescope but disregarding Kepler’s work, showed that Copernicus’s hypothesis was plausible on the grounds that the Earth could no longer be considered as the only centre of rotation. He was, when he most desperately needed it, at a loss to offer any definite proof.

    Newton offered a plausible physical explanation for Kepler’s Laws, but still there was no actual measurements that showed that the Earth really did move.

    Now, my question is this: why did not Newton, Galileo, Kepler, Copernicus (and all the way back to Ptolemy and before) all start at the point of realising (as Phil has just told us) that the rotation of the stars is out of step with the rotation of the Sun by ONE DAY in a year? To people with their mathematical skills it should have seemed obvious that the simplest explanation was that the Earth rotated on its axis once a day and revolved about the Sun once a year. This could be checked to a high degree of accuracy over centuries without any instruments and would be too precise to be a coincidence. Yet these people spent years wrestling with epicycles, ellipses, and calculus without having any reassurance that the heliocentric hypothesis was almost certainly correct.

    Have I missed something very obvious here?

  11. Slugsie

    It’s a great read, even if it does make your head hurt. I look forward to reading it again in 2013… assuming we are all still alive. #themayanswereright

  12. lepton

    How do we measure PRECISELY when earth reaches its perihelion?

    The best I can think of is to monitor Sun’s spectrum. Any better way?

    Happy 2012!

  13. ameb

    Happy new year!
    Did you know Iranians are using the tropical year for long time? I keep seeing people keep speaking about this kind of calendar without mentioning anything about Persian calendar. There should be a lot of information available about it beside wikipedia. Here is an example:
    http://aramis.obspm.fr/~heydari/divers/ir-cal-eng.html

    BTW, this is my very first comment on your blog after years of following it. Thank you very much for keeping us updated all of these years with the very nicely written articles.

  14. um3k

    I prefer 10^7.499111523, personally.

  15. A post worthy of repeating. I wish everyone resolved that each year they will observe science more and more, and how it actually affects their lives.

  16. Grand Lunar

    A great article, Phil!

    An incidently, have you read today’s “Foxtrot” comic?
    Jason laments about celebrating Mercury’s year, Jupiter’s year, and perfers to go by Pluto’s year.

    A fun read.

    Anyway, looking forward to spending another orbit around the sun with your words of wisdom, wit, and rational thinking!

  17. colluvial

    The fault literally lies in the stars, and not ourselves.

    And I think this is, all by itself, a reasonable argument against the existence of a creator. At least a competent one, since the solar system is less accurate than a mechanical clock.

  18. Takeru K

    @4. Tim Gaede & 15. um3k:

    Regarding the number of seconds in a year,

    10^7.5 (or 10^7.499111523) vs. π ×10^7

    Both of you preferred one of the first two options over π ×10^7 because it is more precise/accurate. Please allow me to make an argument for why many use the π ×10^7 number.

    Firstly, it is easier for quick order-of-magnitude calculations (without a computer/calculator). In many cases, the equation/value you are trying to compute might also contain a π in it, so this allows for very easy cancelling. In addition, if this π is the only π in the expression, many astronomers (for these quick calculations) will use π = 3 (also useful is π^2 = 10).

    However, it is indeed not precise. But if you are calculating something exactly now, instead of an approximation, then you would use a computer (or pocket calculator) and the exact value would be used, not 10^7.5.

    π x 10^7 (or 3 x 10^7) gives you easy numbers to work with. The exact values will give you accurate solutions. There doesn’t seem to be an advantage for middle ground values like 10^7.5, unless you are good at doing powers of 0.5 in your head!

  19. Robin Byron

    All this talk of time brings me down a bit. The breathtaking beauty, unimaginable size, distances and time of this universe and all we get is a nanosecond glimpse in our paltry lifetime. I want more time, dammit. Oh well, at least daytime tomorrow will be 33 seconds longer than today.

  20. Björn Lammers

    You had me laughing at “but in the northern hemisphere…”, and once more in the next paragraph. I will point my friends (and enemies) to this article if they ever again ask me about seasons and/or ask me why a year doesn’t have exactly 365 days.

    Happy New Year to you!

  21. Personaly, I use nychthemeron relatively often, but I’m Greek, so that’s to be expected. But if you want some extra ammo in case someone drops it in a conversation, the word is actualy an adverb. It is used whith a verb expressing an action that takes a whole day and night. The greek word that more closely expresses the meaning in the context you are using it for is “ημερονύκτιο” transliterated probably as “emeronyktio”.
    Oh, and happy new year, whatever the length!

  22. George

    ημερονύκτιο=day plus night

  23. Junandharu

    We can measure a year in something else, something earthier, called a culture, a shut-up-and-enjoy-your-holiday-ness thing. But i do love your article!! Happy New Year!!

  24. Eowland Whittet

    In light of all that pi x 10 million stuff, its interesting that there are exactly twice as many seconds in a century as there are inches in the circumference of the Earth at the equator, as close as can be measured allowing for things like the thermal expansion of the planet what with global warming and all.

    At first that might seem like a coincidence until you realize that people have been proud of their ability to accurately measure the Earth’s circumference at the equator since before they started using solar calenders.

    The Romans used a pretty good approximation of 75 milliare or 111 km to a degree, but before they came along the Greeks had come up with the same calculation using the mia chilios or thousand which itself was based on the Egyptians aroura derived from a Sumerian iku.

    One milliare is a mile of one thousand paces, 5000 feet for which the Roman word was pes and the Greek word pous. It was divided by the Greeks into 8 stadions of 600 pous and by the Romans into 8 stadiums of 625 pes but both stadium and stadion were 185 meters.

    The Old English divided their mil into 8 furlongs of 5000 fote like the Romans until the time of Queen Elizabeth who changed the furlong to be 660 feet and the mile 5280 feet which is what made the equivalency.

    http://en.wikipedia.org/wiki/Talk:Proportion_%28architecture%29

  25. >> It’s amazing any astronomers reproduce.

    Why? I guess people prefer to stick to the tired old stereotype of astronomers being socially awkward people, obsessed with Star Trek and wearing the term nerd as a badge of honour.

    Cue article on the mystery on why more young people are not going into science… Sheesh….

  26. Now, my question is this: why did not Newton, Galileo, Kepler, Copernicus (and all the way back to Ptolemy and before) all start at the point of realising (as Phil has just told us) that the rotation of the stars is out of step with the rotation of the Sun by ONE DAY in a year? To people with their mathematical skills it should have seemed obvious that the simplest explanation was that the Earth rotated on its axis once a day and revolved about the Sun once a year

    If the only thing you want to do is explain that, it’s just as easy to say that the heavens as a whole rotate about the Earth once a day and the Sun moves around the celestial sphere once a year. Which is pretty much what they said. From a modern perspective it’s far more physically awkward, but they didn’t have any concept of the physics.

  27. Wzrd1

    Phil, you’ve reminded me of a fair amount that I already knew. Elucidated upon things I know all too well. You’ve reinforced some rather complex math that gave me migraines and confused our calendar horrifically.
    Yet, two things ring clear.
    The rings of the universe in the bible. ;)
    AND, the final item of foremost importance:
    “Yappy Hew Near!”
    For all and one. :D

  28. reidh

    Thanks for reminding me of Side-Reality.

  29. case491

    quote” So there you go. As usual, astronomers have taken a simple concept like “years” and turned it into a horrifying nightmare of nerdy details. But really, it’s not like we made all this stuff up. The fault literally lies in the stars, and not ourselves.” unquote.

    As far as I am aware, after curing my headache and applying the article to the problem, the real fault lies with us and not the stars.

    We are the wobble in an otherwise very organised cosmos. We are short-lived, see (visible) light and can only “hear” a fraction of the full spectrum of waves. Were we longer lived, could see infra-red or hear radio waves, our measure of time would be based on other cycles in our universe. Maybe another interesting article coming up?

    I am a bit late, as always, but I live in the wrong time zone so maybe I was earlier…..???
    Happy New Year to all and as always a fantastic article.

  30. Polo

    Very good article! I really never knew about tropical years until now.
    I think that would be helpful to add how we match our standard years (“gregorian”) to the tropical years. This is why every 100 years there is no leap year (3 out of 4 times anyway), accounting for the slightly less than 365.25 tropical year.
    Happy new year!

  31. JMartin

    Astronomers are the biggest trolls in the world….

    You should post this on 9gag… :(

  32. wally

    There has been some discussion in international timekeeping about the practice of adjusting the synchronicity of the rotational period with the length of the day using leap seconds, and how this can lead to computational and record keeping errors from things as varied as GPS positioning and global stock exchange transaction timings. Any thoughts from The Bad Astronomer?

  33. Zippy the Pinhead

    Have a nice nychthemeron.

  34. Slim

    @11. Alan(UK)

    If the Sun is going around the Earth, there is still going to be a difference of about one day, for the same reason. In that system, in one day, the sun has moved about 1° relative to the fixed stars. So the Earth has to rotate (or rather, the crystal spheres had to rotate) a bit more to have a full day. Just as in the real sun-centered system. They probably said that we had to be at the center, because otherwise why isn’t there any observable parallax in the stars? They didn’t realize just how far away the stars really are.

    Actually, I was thinking about how we measure a year not too long ago, and I realized that this must be why real astronomers don’t use the term light-year even though it makes a lot more sense than a parsec. But if we want to be precise, an AU (used to calculate a parsec) is a lot better defined than a year.

  35. Phil, this paragraph of yours has an error in it:

    “Wait, that doesn’t sound right. You’ve always read it’s 365.25 days per year, right? But that first number, 366.256, is a year in sidereal days. In solar days, you divide the seconds in a year by 86,400 to get 365.256 days.”

  36. Gwif

    Don’t forget that other cultures have different years as well. For example, the Islamic year is based on the moon – 12 lunar months. (354 or 355 days)

  37. RobT

    Phil said
    “First, I will ignore a few things. For example, time zones. These were invented by a
    sadistic watchmaker, who only wanted to keep people in thrall of his devious plans.”

    Keeping with the tongue-in-cheek tone of that sentence, here’s my response:

    I think time zones are better than the alternative; there’s a reason they were standardized (thank you Sir Sanford Fleming). If every city kept their own time based on their solar day, like they used to do before the railroads, then timetables would be off – try having a set time for trains, planes or TV when everyone’s time is off by a few minutes. Or if everything was referenced to GMT or UT then everyone would have to do conversion to their own time anyway. Try catching a TV show when it starts at 8:12 “in your region”.

    Now, if we could only get Daylight Savings Time as the standard and get rid of the stupid time change twice a year. Why DST? I like it better here in the northern climes when the sun doesn’t set at 16:30, as it does in the winter; 17:30 would be much nicer. That way most people aren’t driving to and from work in the dark.

    Interesting article, either way.

  38. avout

    Interesting about the word for ‘day and night’, I have thought of this before. Since I’m Swedish I’ve found the lack of an english word for 24h somewhat strange. In Swedish we have the word ‘dag’ = day, and the word ‘dygn’ = 24h. Both of these are common words used pretty much all the time..

    Gott nytt år!

  39. #40 RobT:
    I don’t know what your latitude is, but…
    Sometime in about the 1960′s, the UK tried exactly what you suggest, keeping British Summer Time ( GMT + one hour ) all year round. The result was that around the winter solstice, it didn’t get light in the morning until about 9 a.m., so children had to walk to school in the dark.
    So the idea was dropped, and we reverted to the twice yearly change.

    Since you brought up daylight saving time; that was first done in Germany after the end of the Second World War. It was the idea of their famous Chancellor… Dr. Adenauer. :-)
    Sorry. I’ll go now.

  40. OK most of all this seems to make sense about orbits and gravity and all of that. No one explains why there has to be a solar plane that the planets follow. If these scientists can detect the wobble of other stars caused by gravity of orbiting planets. Why can they not find a wobble of our sun? It seems to be much closer. What is up with the tides anyway? When I was about 17 years old NASA sent men to the moon. This trip took about 3 days. There did not seem like much going on for those 3 days. At the beginning of the third ray I can remember Walter Cronkite making a big deal about the spaceship passing from earth’s field of gravity into the moon’s field of gravity. From that point on the spaceship would be falling towards the moon. If that is as far as the moon’s gravity reached how does the moon’s gravity have anything to do with the tides? If you look at the tables for tides you will find that high tide comes twice a day. So if I am standing on the beach and the high tide is occurring, it is also happening on the other side of the earth. I’m not real smart, but how does the moon have anything to do with the tides on the opposite side of the world?

  41. #43 Tony:
    1. The planets’ orbits are all in roughly the same plane, as a consequence of the way in which the Solar System formed. It formed from a huge cloud of gas, which condensed under gravity and began to rotate. That rotation gradually flattened the cloud into a disc. It’s all about conservation of angular momentum.
    2. Who says they can’t detect the wobble of the Sun? Of course they can – but there’s no need for anyone to measure it, as we know the orbital periods of the planets very accurately.
    3. I’m sure there are plenty of explanations of the tides on the internet – including a very good one somewhere by Dr. Plait himself, if you care to search for it.
    You seem to have a serious misunderstanding of gravity! Your phrase “as far as the Moon’s gravity reached” is totally meaningless! Firstly, it’s a complete fallacy to say that any one body “exerts a gravitational pull on” another. What actually happens is that every two objects – in this case, the Earth and Moon – exert a mutual gravitational force on each other, which is directly proportional to the product of their masses, and inversely proportional to the square of their distance apart. So “as far as the Moon’s gravity reaches” is in fact to infinity, but it becomes weaker by the inverse square law – at double the distance, the attraction is reduced by a factor of four, etc.
    Now for your point about the Apollo spacecraft. You’re thinking of the point at which the Moon’s gravity balanced that of the Earth. Each spacecraft was boosted by its rocket to the Earth’s escape velocity, about 25000 mph, then the rocket cut out, and the spacecraft was left coasting. So it was being constantly decelerated by the Earth’s gravity, and at the same time, accelerated by that of the Moon. As the Earth’s gravity, at its surface, is six times that of the Moon, it follows that it predominated for most of the way, so the spacecraft slowed down. At a point roughly 5/6 of the way to the Moon – when the spacecraft had slowed down to a mere 2200 mph – the gravitational acceleration due to Earth and Moon became equal. Up to that point, the spacecraft was being slowed down by Earth’s gravity; after that point, it was being accelerated towards the Moon, as the Moon’s gravity now predominated.
    On the return journey, the exact opposite happened; the spacecraft was boosted by its engine to the Moon’s escape velocity, then was slowed down by the Moon’s gravity until it reached that point of balance, then was accelerated towards the Earth after passing that point.
    So it was nothing to do with “as far as the Moon’s gravity reaches”; it was to do with when it predominated over that of the Earth.
    The Moon has everything to do with the tides! The Earth and Moon exert a mutual gravitational pull on each other. If you consider the water in the oceans as a separate body from the solid body of the Earth, then there is also a mutual gravitational pull between that body of water and the Moon. This causes a “bulge” in the body of water, which is elongated in the direction of the line between the Earth and Moon, and compressed in the direction at right angles. Think of it like a sphere being stretched into an ellipsoid – so the bulge occurs on the opposite side of the Earth, as well as on the side facing the Moon. As the solid Earth rotates daily, it rotates with respect to the bulge; places on its surface facing the Moon, and those 180 degrees away, pass under the bulge, causing high tide, while places 90 degrees away pass under the narrowest part of the ellipsoid, causing low tide. Hence we have two high and two low tides per day.
    That’s a very brief precis. Please do a web search for a more detailed explanation; it’s bound to be in Wikipedia, and as I said, you can find it somewhere in Dr. Plait’s blog.
    Hope this helps.

  42. Matt B.

    Careful. The Gregorian year is not the same as the tropical year, it’s only a calendrical approximation of the tropical year, and in fact differs by a day about every 1,190,827 years. I think Russia is the only country not using that calendar (perhaps the former SSRs use it too), and theirs hasn’t technically differed yet.

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