Here comes an improvement to my diagram of our motions in space.
Janette asked: “Can you add all these speeds of motion and say we are travelling at 3,069,700 km/hour?” You can’t add them all simply, since they are in different directions. You can add two at a time, and I’ve been thinking how to do so.
You row your boat straight across a river. But the river is flowing at twice the speed of your rowing. So you reach the opposite bank some way downstream.
The red arrow is the vector of the boat, the blue arrow is the vector of the current, and the black arrow is the resulting combined vector. Its length is not that of the other two vectors added. A way of looking at it is that the blue vector drags the red vector downstream, to the position shown by the orange arrow.
This is the special case in which the vectors are at right-angles to each other, so that their envelope is a rectangle, and the length of the resultant vector is easy to calculate (from Pythagoras’s law). But the two vectors can be at any angle to each other.
And then they fill out a skewed quadrilateral and the length of the resultant is not so simple to calculate.
Now, in our cosmic picture, the two great vectors, that of the Sun’s motion (in the present part of its orbit around the center of the Milky Way galaxy) and that of the Local Group of galaxies’ fall toward the Great Attractor, are wide apart. They are at these right-ascensions and declinations:
21h 12m (= 318°), 48°
16h (240°), -60°
These points are 125° apart. One is in Cygnus, a high-northern constellation, and the other is far south, on the border of Norma and Triangulum Australe. Is the resultant direction half way between them? (That would be about on the Aquila-Scutum boundary, not far from the direction toward the center of the Milky Way.) No, because the speed toward the Great Attractor is more than twice as great. So our resultant direction in the cosmos has to be farther south, in Scorpius.
As for how a third vector, such as Earth’s motion in its orbit, can be added – how such vector diagrams can be stacked, as surely they can – I don’t yet know.
The two thousand, nine hundred, and eleventh day of May
Nobody answered my conundrum about what May 2911 would really be – I ought to have offered a prize, such as a holiday in our B-and-B on Mars. I’ve found the answer by a sort of brute force: turn May 1 into a Julian date, add 2911, and turn that Julian date back into a calendar date. I could only do it by writing a little program, which could be called “sillydates.for.” It found:
2021 May 2911 = 2029 April 19 Thursday
2022 May 2911 = 2030 April 19 Friday
2023 May 2911 = 2031 April 19 Saturday
That the day numbers do not vary, while the day names move on regularly, is presumably because in such a long span there is an unchanging number of leap days.
The silly experiment illustrates something a little more serious: the efficiency of the Julian date system, a plain count of days. Trying to count 2,911 days through nine printed calendars would drive you more than silly.
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This weblog maintains its right to be about astronomy or anything under the sun.
With apologies to Freud, we seem to be developing a psychodynamic theory!
Not to beat a dead horse, but I think Dan is right. If the question is meant as: Which calendar date would be equivalent to May the 2911th?
Make the question dummer, like, what calendar date would be May the 31st? – If you take the inclusive route – you get June 1st.
My pocket calculator has a ddays function (also date+ and date-) and it reckons date exclusive of the beginning date – because the ddays of 2022-05-01 and 2022-05-01 is, of course, zero, not 1. Of course the internals of the function is also Julian day conversion and arithmetic – but HP chose to give an exclusive result. It’s the old fence problem – of posts vs rails. btw, I made up the “baker’s gross” as a joke – and it was just a delight to have this fellow immediately answer 13^2 – at our first meeting eleven years ago.
Guy, I am lucky to live with a calendrical savant (also in other areas) and when we are still suffering frost and cold in spring – I have been known to refer to the date as “it’s February 52nd” for instance – this makes him crack a smile and giggle. He is also a delight to ask such corny questions as “What’s a Baker’s Gross?” (169). Separately, I wonder if you know of anyone else who thinks of the unit of the “Platonic Day”. Of course this would be the factor-rich number: 25,920 days. During this time* one witnesses a precession of 1 degree – which has the amazing effect of causing the Platonic Year to suddenly seem not so incomprehensibly long. * I know, I know, it’s really something like 25,770 days or such, but 25,920 is just a more beautiful number and is close enough. Waiting to see the possible meteor storm – The 1966 Leonids are one of my earliest memories.
I knew of a baker’s dozen (13) but not a baker’s gross.
Yes, this is known in engineering mechanics as vector addition.
Dan Cummings answered April 20, 2030. One day off from your answer. He didn’t explain how he got that date.
Vectors are a great metaphor for life. Vector analysis is an essential aspect of my work as a psychiatric social worker. I try to get a sense of where each client is headed in life. If they’re basically headed in a good direction, with fair winds and following seas, my job is easy, just support, encourage, and provide resources. If they’re headed in a bad direction I try to figure out how to nudge them onto a better course. Sometimes this is possible, sometimes not. And the winds may be blowing in a different direction tomorrow, for good or ill.
Apology to Dan! I must have seen his answer, but it was so brief I may have confused it with other brief things that sometimes come, such as “pingbacks”.
I hope Dan will tell us how he calculated. I think his answer is one day wrong because you don’t just subtract the first date from the second, but subtract one more. For instance the span 1 to 11 INCLUSIVE is not 10 but 11. We were talking about the inclusive span May 1 to May 2911.
So, Dan, you only get a holiday in our B-and-B on the Moon.
Vectors in psychology: yes, very applicable, and they, too, add to or compound each other. A person may have a wanderlust vector, a good-doing vector, a greed vector, a sex vector, a creative vector, they are in conflicting directions and have different – and fluctuating – magnitudes, and resultant behaviors are produced by how they pull against each other.