Question

My coworker and I were bored with time to kill and I was saying it's a coincidence that there are 365 days in a year and that 360 is a highly divisible number. He seemed to disagree, he thought it was chosen specifically because 360 is the number closest to 365 that's highly divisible. We got to thinking, what would be good criteria for determining a highly divisible number near to the number of days it takes for other planets to go around the sun, for instance Mars, that could then also be used for making a practical calendar for that planet?

Answer 1

I think it strongly depend on the dynamic of the planet
and how close to the sun it is
and the power of gravity of each the planet and the son and how they effect each others
Too many factors determine that
we cannot decide which one is true but they all connected
yet there is no obvious scientific reason
Earth regular year has 365 days
where other planet like Jupiter has ten thousand
and Venus has actually less than 1 (Lol)
that's how it is
No obvious reason

Answer 2

Haha well for the most part it doesn't matter because to their respective planets, it's a constant. I'm not talking about determining the period of planets, I'm looking for a way to determine a number that's highly divisible near any arbitrarily given number.

For instance, if we look at other alternative numbers with lots of divisors near 365 we have:
\[360=2^3*3^2*5\]\[364=2^2*7*13\]\[368=2^4*23\]

So even though 360 is further away from 365 than the other numbers are with only 1 and 2 more prime numbers than 364 and 368 respectively, for some reason we've picked it in the past cause it was nicer.

I'm not really talking about astrology here though, I'm really just looking for ideas and a fun way for:

"Given an arbitrary number, what's the nearest number that's only divisible by 2, 3, 5?"

Or maybe something else similar and related. Maybe we can even change this question to:

"What should the Martian calendar look like when people start living on Mars?"

Answer 3

ooh that's really fun question

Answer 4

am not sure about this
but if we can determine how we calculated the calendar on Earth and based on what factors then probably we can apply
that similar method for Mars (taking into consideration the special factors of Mars)
Am probably the most awful in this lol but just saying

Answer 5

Yeah that seems pretty reasonable actually! I was just looking at the Mars year, it has 687 days, so:

\[687=2^2*17\]
not very good for splitting up your calendar into months and weeks I think. So I did a little thing to calculate the number of prime factors a number \(n\) has with the function: \(\Omega(n)\), and I only looked at values that were within 20 of the number of days with at least 4 primes in it. Here's what I got to start us off:
\[\Omega(672) = 7\]\[\Omega(675) = 5\]\[\Omega(676) = 4\]\[\Omega(680) = 5\]\[\Omega(684) = 5\]\[\Omega(686) = 4\]\[\Omega(688) = 5\]\[\Omega(690) = 4\]\[\Omega(693) = 4\]\[\Omega(696) = 5\]\[\Omega(700) = 5\]\[\Omega(702) = 5\]\[\Omega(704) = 7\]

Answer 6

So like for instance these furthest away ones here that have 7 prime factors are sorta like interesting cause they're further off from the number of days there are (so more irregular numbered months like earth has 30 and 31 and a 29 day month) although since the year is longer we can fit in more or longer years into our calendar so it might not be so bad. Haha. Here are the prime factorizations of the most interesting numbers (in my opinion!):

\[672=2^5*3*7\]\[684=2^2*3^2*19\]\[690=2*3*5*23\]\[700=2^2*5^2*7\]

Answer 7

i guess then the concepts of week, month, year would change
weeks could be 8 days in Mars or more or less
i don't think they will follow the same rules on Earth
Every planet vary from the other not only by gravity but from your calculations also the time!
quite interesting but that's what it would be
it would strongly vary from Earth since the day is not even 24 hrs there the whole calculations would change and concepts too.

Answer 8

Yeah, so like for instance we could have like 23 months with about 30 days each still and break those up into weeks like normal more or less if we wanted

Answer 9

I guess since the orbit is not as regular as ours and it spends more time away from the sun than near it (well slightly) that's something to consider.

also since they go around the sun at different speeds, there's a time when Mars and Earth are both on the same side of the sun (close together) and when they're on opposite sides of the sun (far apart) so it might be nice to incorporate this into the calendar as when the good time is to leave and arrive between planets. :P

Answer 10

Lol yeah agreed
it would be like when we figured the leap years on Earth
there would be some new events as you mentioned
requires us to set them appropriately
but we don't need to worry about that now lol we still have long way to live on Mars
i mean let's fix our Earth 1st :P

Answer 11

lol hey if I wanna waste my time playing around with numbers instead of playing video games, whatever