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February 2

Equation for Period of Orbit

A link to the appropriate Wikipedia article will be fine if it answers my question. What is the equation, assuming a circular orbit, that gives the period (time) of an orbit if the mass of the primary is known, the radius of the orbit is known, and the gravitational constant G is known (which of course it is)? That is, please provide the equation with the result being the period (in time units). Alternatively, given the orbital period in time units and the mass of the primary, what is the equation that will specify the radius of the orbit?

Thanks. Robert McClenon (talk) 04:23, 2 February 2018 (UTC)[reply]

See Orbital period#Small body orbiting a central body. Explanation: if the orbit is circular, then the centrifugal (from motion) and centripetal (from gravity) forces must be in balance. Therefore

GMm / r² = mv² / r

GM / r = v²

v = √GM / r

On the other hand, the period T can be calculated from the orbital speed and circumference

T = 2r

π

/ v

T = 2r

π

/ √GM / r = 2r

π

√r / √GM

T = 2r^3/2

π

/ √GM

You can then turn this around to get the answer to your last question:

r = (T²GM / 4

π

²)^1/3

An interesting consequence: the orbital speed and period do not depend on the mass of the orbiting body (m). Hence, the orbited body's mass can be estimated by observing the radius and revolution period.

I believe the derivation for an elliptic orbit shouldn't be much harder, but as I haven't done physics beyond high school, I won't chance it. 93.136.124.10 (talk) 05:36, 2 February 2018 (UTC)[reply]

93.136 says that "the orbital speed and period do not depend on the mass of the orbiting body". But those equations are for a small orbiting body, meaning one whose mass is negligible compared with the central body. In fact, if the smaller body is not that small, you just have to substitute the total mass of the two bodies for M in the final equations. See Orbital period#Two bodies orbiting each other. --70.29.13.251 (talk) 02:35, 3 February 2018 (UTC)[reply]

An elliptic orbit has the same period as a circular orbit with the same long diameter (one of Kepler's big three observations), but I can't prove it. —Tamfang (talk) 00:22, 3 February 2018 (UTC)[reply]

The orbital period which comes out of these equations is a mean, i.e. you are starting with the assumption that the body moves in a circle at constant velocity. That is the essential feature of the "mean longitude" argument in the tables. In The History of the Tropical Year celestial mechanics experts Jean Meeus and Denis Savoie give average intervals between vernal equinoxes at various dates but they describe them as "mean" intervals although the lengths vary widely in Ephemeris Time (which is constant). In Ephemeris Time the mean interval between vernal equinoxes is 365d 05h 48m 45s and always has been. The authors give no explanation of how they calculated their figures and, despite extensive investigation, nobody else has been able to find out either. Should information which cannot be verified be allowed to remain in the article? 2A00:23C1:E083:8201:9875:F878:985D:A2C7 (talk) 05:25, 3 February 2018 (UTC)[reply]

We're getting off topic, but Wikipedia's role as an encyclopedia isn't to verify that this is absolutely, truly, "the real number" -- only to tell readers that a book by Meeus and Savoie said it is the real number. If you can find more, better sources you might be able to push that one out, though truly, a good encyclopedia would never discard a valid source from consideration entirely. Wnt (talk) 12:37, 3 February 2018 (UTC)[reply]

Your own calculation of the average over 2000 years verified the Meeus figure (though you deliberately got it wrong). Dbfirs 19:06, 3 February 2018 (UTC)[reply]

Thank you. I know that the orbital period does not depend on the mass of the satellite. It is interesting that, to determine the mass of a light object, you have to use a heavy object; and to determine the mass of a heavy object, you have to use a light object. A light object is one like a grain of salt, a breadbox, a human, a truck, a fully loaded 747, or an artificial satellite, whose gravitational field is negligible for other purposes. A heavy object is one like Luna, or Mars, or Sol, whose gravitational field is non-trivial. To determine the mass of a grain of salt or a 747, you measure its weight on the Earth, and weight is a function of mass and of planetary gravity. (This makes it hard to determine the mass of a piece of debris in space, because weight is measured by resistance, not by observing an orbit.) To determine the mass of a heavy object, you have to observe something orbiting it. The mass of Mars was much better known in 1878 than in 1876; the masses of Deimos and Phobos were and are still just estimated, but the mass of Mars can be determined by their orbital parameters. Robert McClenon (talk) 22:00, 3 February 2018 (UTC)[reply]

I don't think we need to look further for a source than Meeus and Savoie themselves. In the cited paper they say:

Finally, according to Danjon the tropical year is the time needed for the Sun's mean longitude to increase by 360°. This is the definition which is adopted nowadays.

They also cite Smart's Textbook on Spherical Astronomy:^[1]

The tropical year is defined to be the interval between two succesive passages of the sun through the vernal equinox.

The two measurements are not the same - "the time needed for the Sun's mean longitude to increase by 360°" is 365d 5h 48m 45s. "The interval between two successive passages of the sun through the vernal equinox" fluctuates wildly. This means that either of both of these definitions is wrong. We can remove the anachronism by amending the first definition to read:

The mean tropical year is the time needed for the Sun's mean longitude to increaase by 360°.

The vernal equinox is a direction in space (the place where the plane of the Earth's orbit intersects the plane of the celestial equator). It is also a time - the time when the sun reaches that place. The mean sun reaches that place at a time known as the mean vernal equinox - that is how the distinction between the two is made. Our article tropical year introduces new errors. The lead says, correctly:

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.

It then says (correctly):

The entry for "year, tropical" in the Astronomical Almanac Online Glossary (2015) states: the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons ...

Then comes the error:

An equivalent, more descriptive definition is "The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox of date). Whenever the longitude reaches a multiple of 360° the mean Sun crosses the vernal equinox and a new tropical year begins.

Wrong. That should read "Whenever the longitude reaches a multiple of 360° the mean Sun crosses the vernal equinox and a new mean tropical year begins." The mean tropical year is divided into four equal seasons, each 91d 7h 27m 11s in length. The starting date of each season is dependent on the leap year cycle, but is roughly 23 March, 22 June, 22 September and 22 December. The actual time each equal season starts is tabulated in almanacs.^[2] Note that in the example the time adopted is twelve hours in advance of Greenwich. The reason for the tabulation (apart from them being much easier to calculate than astronomical seasons) is that they are used to calculate which full moons are "blue moons" (the full moons are seasonally named and the blue moon is the third in a season which has four). There is a popular misconception that a blue moon is the second full moon in a calendar month. This is wrong for three reasons:

Not everybody uses Gregorian calendar months. The tropical zodiac is the same everywhere.
Astronomically a blue moon occurs at an average of about every 33 1/2 months (32 1/2 calendar months) because the lunar month is about a day shorter than a calendar month and a calendar month averages about 30 1/2 days. Using the mistaken definition blue moons can come 59 days apart.
In most solar calendars the calendar months are aligned with the seasons. In the Gregorian calendar they aren't.

Meeus himself states (on page 179 of his book Astronomical Algorithms) that the formulae he provides for calculating seasonal lengths give "the true equinox and solstice times". If we can demonstrate that the lengths (alleged to be mean lengths in the article) are derived from the formulae then the article is wrong. We can do this. Dbfirs notes that Wnt calculated the average time between vernal equinoxes over 2,000 years (i.e. Wnt accepted these were averages of true times and not derived from the tables of mean motion) and "deliberately got it wrong" although Wnt "verified the Meeus figure". That's Dbfirs' POV - everyone else would say that Wnt deliberately got it right. The results of the investigations are recorded in the archive. One editor copied in the formulae, explaining that you first calculate the "mean equinox", using "the relevant expression in Table 27" of the book. You then apply "corrections provided in the chapter". The question is then raised "Is the mean equinox the instant when the sun reaches the location referred to as the mean equinox of date?" I don't know why that question was raised because by definition the "observed" equinox is the instant when the sun reaches the location referred to as the mean equinox of date. It is of no matter, however, because the editor answered the question in the negative. He did this after calculating the moment of the vernal equinox in 2001 using Meeus' Table 21A and Table 21B. The article gives a figure for "Year 2000" in the table of "mean time intervals" "Between two Northward equinoxes" of 365.242 374 days. That is exactly the time the formula gives for the length of the 2000-2001 true (astronomical) vernal equinox year, 365.242 374 04 days (to six significant figures). Bingo. Quod erat demonstrandum. For the time of the true 2001 equinox (calculated from the formulae) the editor got the value of March 20d 13h 16m 55s. This compares to the astronomical time March 20d 13h 30m 59s. The editor noted a discrepancy of 13 minutes but then said he had miscalculated and the discrepancy was only 103 seconds.

To round off the investigation I decided to calculate the true length of the vernal equinox year AD 1000 - AD 1001 using both the formula for "Years -1000 to +1000" and the formula for "Years +1000 to +3000". The first formula gave 365.242 137 4 + 0.061 34 + 0.001 11 - 0.000 71 = 365.303 877 4 days. This is so wildly inaccurate that I didn't bother to check what value the second formula would have produced. 2A00:23C1:3180:8301:A133:CEE0:60C3:5741 (talk) 13:58, 6 February 2018 (UTC)[reply]

References

^ Smart, W M (1990). Textbook on Spherical Astronomy. Cambridge. p. 132. ISBN 0-521-21516-1.{{cite book}}: CS1 maint: location missing publisher (link)
^ Olson, Donald W; Fienberg, Richard Tresch; Sinnott, Roger (27 July 2006). "What Is A Blue Moon?". Sky and Telescope.

Meeus, J.; Savoie, D. (1992). "The history of the tropical year". Journal of the British Astronomical Association. 102 (1): 40–42. {{cite journal}}: Invalid |ref=harv (help)

Omega 3

I read that omega 3 can help dry eyes, which I have, especially the omega 3 fatty acids DHA and EPA. Since I hate fish which is the only real source of DHA and EPA, I was reading up on this. There are other supplements of DHA but not alot for EPA, and on wikipedia it appears to say that EPA is converted to DHA, so does this mean EPA is not needed? But it also says that ALA another omega 3 fatty acid is converted to EPA and DHA, so I am confused as to if EPA itself is necessary as a nutrient.--User777123 (talk) 05:23, 2 February 2018 (UTC)[reply]

Have you asked your eye doctor? ←Baseball Bugs ^{What's up, Doc?} carrots→ 06:16, 2 February 2018 (UTC)[reply]

I found one clinical study supporting this as treating for dry eye disease.[1] Krill oil was mentioned as a new thing multiple times in media lately. Cod liver oil also contains omega 3 fat (20%) and has a long history as medicine. I guess that counts as "fish oil". To be fair most medicines tastes awful too. I know cod liver oil is sold in tasteless capsules you can swallow so you dont get to taste it unless you bite one open. --Kharon (talk) 06:31, 2 February 2018 (UTC)[reply]

I can't swallow pills, I have tried chewing up fish and krill oil pills and it is terrible.--User777123 (talk) 07:12, 2 February 2018 (UTC)[reply]

We can't give you advice for your dry eyes (after all, we've not seen them), but eicosapentaenoic acid is generally reckoned as a precursor to docosahexaenoic acid. See [2] To be sure, that doesn't mean that taking DHA can't have an indirect effect on its level; I can't say in which direction at the moment. Alpha-linolenic acid is a precursor to both, apparently not that effective though. I mostly think of that one in terms of breast cancer chemoprevention, though I once saw something about decreased mouse mammary gland development during embryogenesis that struck me as potentially lamentable. Scratching my memory about hemp oil I found this hopeful missive about stearidonic acid in hemp potentially being a closer precursor to EPA. I haven't really chased that rabbit far - the last time I played with hemp oil was around 1990, when it was a fairly nasty way to try to cook spaghetti, and I don't know how good a source it really is. I see there are pure EPA supplements online, and if cost is less concern than pill-swallowing I suppose you could buy them and try to mix the oil into something or other. Use your imagination, but not high heat. Wnt (talk) 13:11, 2 February 2018 (UTC)[reply]

We can not give medical advice here, however, if you can't stand seafood (you may be histamine sensitive), Evening primrose oil is a very good precursor. One's mitochondria can easily convert that into the oils you need. You can get it in gelatin capsules to swallow. Then migrate slowly to cheaper flaxseed and hemp and see how you get on. Also, your home may be very dry. A relative humidity at or below 40% will aggravate dry eyes – so get a meter and measure it. Aspro (talk) 16:24, 2 February 2018 (UTC)[reply]

nurse watches, lapel watches

When did those watches (upside down and worn pinned to the lapel or apron) appear with nurses in (a) the UK and (b) the US? Could there be another country, where these types of watches were "invented"? THX! GEEZER^{nil nisi bene} 15:41, 2 February 2018 (UTC)[reply]

According to this, lapel pin watches came into vogue in the late 19th and early 20th century, they have an example there from 1901. --Jayron 32 15:44, 2 February 2018 (UTC)[reply]

This forum post discusses the history. It may lead you somewhere interesting. --Jayron 32 15:46, 2 February 2018 (UTC)[reply]

Thanks! Hopping on from there I found this. Case closed! GEEZER^{nil nisi bene} 12:00, 4 February 2018 (UTC)[reply]

[1] Smart, W M (1990). Textbook on Spherical Astronomy. Cambridge. p. 132. ISBN 0-521-21516-1.{{cite book}}: CS1 maint: location missing publisher (link)

[2] Olson, Donald W; Fienberg, Richard Tresch; Sinnott, Roger (27 July 2006). "What Is A Blue Moon?". Sky and Telescope.

[1]

[2]