Re: Titan Time
Zefram said: >> There's nothing at all wrong with the radian - but there is a reason >> calculators let you switch between degrees and radians. Each is best >> for particular purposes, > Certainly the radian is best for some purposes. But the degree? Is there > some inherent feature of the circle that makes it particularly natural to > divide it into 360 parts? Not really. Personally, I like the mil: 6400 mils in a circle, and a mil is close enough to a milliradian that you can use the usual tricks (a mil subtends about a metre at a kilometre). -- Clive D.W. Feather | Work: <[EMAIL PROTECTED]> | Tel:+44 20 8495 6138 Internet Expert | Home: <[EMAIL PROTECTED]> | Fax:+44 870 051 9937 Demon Internet | WWW: http://www.davros.org | Mobile: +44 7973 377646 THUS plc||
Re: Titan Time
Rob Seaman wrote: >There's nothing at all wrong with the radian - but there is a reason >calculators let you switch between degrees and radians. Each is best >for particular purposes, Certainly the radian is best for some purposes. But the degree? Is there some inherent feature of the circle that makes it particularly natural to divide it into 360 parts? I don't think angle quantities need particular divisors any more than length quantities do. For that matter, dividing the circle into 360 parts for some purposes and then 24 for others (solar time, right ascension) is pretty annoying. It would be nice to be able to calculate LMT = UT + longitude without having to switch units in the middle. >...leading to the need to rely on pico, femto or atto spheres on a >day-to-day basis? For some purposes, yes. In astronomy, I can't really visualise a square arcsecond, but expressing it as 1.9 psf puts it in proportion. > also the ability to express right angles and a >multitude of other special values of trigonometry, leading to >expressions like cosine (166.667 mcr) = one-half. The right angle is, of course, 250 mcr. As for arccos(1/2), I'm as happy to express it as "1/6 cr" as to express it as "1/3 _pi rad". -zefram
Re: Titan Time
Zefram wrote: the radian is not a very practical unit. There's nothing at all wrong with the radian - but there is a reason calculators let you switch between degrees and radians. Each is best for particular purposes, just as interval time and time-of-day are best for different uses. See also natural and common logarithms. Or even the continuing value of Newtonian mechanics in the age of Relativity. I prefer to use the circle: 1 cr = 2 _pi rad. Similarly, for solid angle, the sphere: 1 sf = 4 _pi sr. ...leading to the need to rely on pico, femto or atto spheres on a day-to-day basis? 83 mcr (millicircles). That gives me a good image of where the sun is. Fine. Glad for the acknowledgment that the position of the sun in the sky matters. I prefer to cut everything decimally, including the circle and the day. Actually I might prefer to cut everything octally, but decimal is the dominant standard so let's use it. Consistency is the key. Point "the Google" at "consistency emerson" for the canonical quote on this subject. For angles, I'll merely point out that you appear to be willing to sacrifice not only the 24 hours in a day (what would Jack Bauer think?) – but also the ability to express right angles and a multitude of other special values of trigonometry, leading to expressions like cosine (166.667 mcr) = one-half. And my kid thought trigonometric identities were dubious before... I doubt even the ITU would claim authority over the definition of pi :–) Rob
Re: Titan Time
Rob Seaman wrote: >Presumably folks who dismiss sexagesimal Sumerian units for clocks >would also welcome the deprecation of degrees for measuring angles. Oh yes. But the radian is not a very practical unit. I prefer to use the circle: 1 cr = 2 _pi rad. Similarly, for solid angle, the sphere: 1 sf = 4 _pi sr. >and local time (since this is an >angle, too) as 0.5236 radians past midnight? 83 mcr (millicircles). That gives me a good image of where the sun is. > I prefer my pi cut into >12 slices. I prefer to cut everything decimally, including the circle and the day. Actually I might prefer to cut everything octally, but decimal is the dominant standard so let's use it. Consistency is the key. -zefram
Re: Titan Time
John Cowan wrote: MAPS: In general the flybys around T20 are relatively similar. They approach over 35degrees latitude, ~135degrees west longitude (moving from north to south) and local time is around 2 am. Bizarre. So each Titan local day is 24 local hours long, where an hour is about 57.4 ksec? Which of these notions would you prefer to discard – the idea that local planetary time is divided into 24 parts, or that one of those parts may not be 3600 SI seconds long? In a solar system full of dozens of rotating spheroids, what overarching concept of timekeeping best ties all the local clocks together? Oh! I know – let's ignore the big shiny signpost in the middle! Surely every space mission isn't tasked with inventing not only a new clock, but also a new kind of clock? Surely it would be better to adapt prior art to new conditions? On this tidally locked moon, one can make the case that descriptors like midnight, noon, sunrise and sunset gain an even greater importance precisely because they are extended by a factor of 16 in duration. How then best to convey an illumination similar to 2 am local time on Earth, rather than by calling it "2 am"? Should the Earth be deemed a special case whose rotational clock will be allowed to drift by 54,000 arcseconds precisely over the historical period that humanity is exploring, visiting and perhaps colonizing other planets and moons? Why? My personal mnemonics: you can be no more than a ksec late for an appointment in American culture without anyone making a fuss; a Msec is a reasonable length of time for a single work assignment; a marriage is doing very well if it lasts a Gsec (mine is at 0.85 Gsec and counting). And any good university library will be chock-a-block with utopian screeds for metric calendars and clocks. Presumably folks who dismiss sexagesimal Sumerian units for clocks would also welcome the deprecation of degrees for measuring angles. So the Cassini operations staff would be expected to report its ground track as 0.6108N 2.356W, and local time (since this is an angle, too) as 0.5236 radians past midnight? I prefer my pi cut into 12 slices. The pragmatic engineers who pilot spacecraft pay little attention to astronomers' whims when choosing what standards to use. They must have had some other reason for not specifying those "standard" units that were baptized during the Reign of Terror. Rob
Re: Titan Time
Peter Bunclark scripsit: > MAPS: In general the flybys around T20 are relatively similar. They > approach over 35degrees latitude, ~135degrees west longitude (moving from > north to south) and local time is around 2 am. Bizarre. So each Titan local day is 24 local hours long, where an hour is about 57.4 ksec? My personal mnemonics: you can be no more than a ksec late for an appointment in American culture without anyone making a fuss; a Msec is a reasonable length of time for a single work assignment; a marriage is doing very well if it lasts a Gsec (mine is at 0.85 Gsec and counting). -- Take two turkeys, one goose, four John Cowan cabbages, but no duck, and mix them http://www.ccil.org/~cowan together. After one taste, you'll duck [EMAIL PROTECTED] soup the rest of your life. --Groucho
