Pal's birthday today 10/31 2:00 EST. 1964. When will he have really made 42 complete revolutions about the sun

Question

Categorization of this question was tough, and as there was no astrophysics subcat...

Looking for an independent confirmation of my solution Puzzling- thanks - he doesnt believe me...

Within the hour is fine...

(assume his relative displacement on the surface of the planet is 0.)

puzzling-you're a half a day off of your calc for the number of days old he is at t≡0 (mod birthtime)

generally first...
if a year were a perfect 365 days, his birthday point of integral revolutions would be exact...

but since we're in a 4-year cycle of (needing to) add a day, and since were greater than 2 years into that cycle, we must be at least a half a day off.
No?

no math needed to this point. rotation about the earth can be included after this point.

The number of days elapsed is 15,340.5 not 15,340 !
Remember, we're half-way into another 4-year cycle, so we're 1/2 a day's revolution off now. (This half a leap day hasn't been accounted for)

Answer 1

Let me work on it...

Well, I started looking at information on 'heliocentric planetary positions', etc. trying to figure out the position of Earth on 10/31/1964 2:00 EST compared to 10/31/2006 to figure out when they would have the same values. This got me way over my head with universal coordinated time, latitudes, longitudes, etc. I don't think it need to get that complicated.

Finally I tried figuring out the number of elapsed seconds to divide by the seconds in a year...

Okay, here's what I figured out:
Between 10/31/1964 and 10/31/2006 is 15,340 days or 1,325,376,000 seconds.

Google gives the period of a year as 31,556,926 seconds.

Dividing the two I get 41.9995281 years.

The difference between 42 and this number is 14,892 seconds. That would mean you would need another 4.13667 hours until the Earth has made 42 complete revolutions around the sun.

That works out to 4 hours 8 minutes 12 seconds later or around 10/31/2006 at 6:08:12 EST.

What did you calculate?

Edit: I see where you are coming from with leap years, etc. First, 42 years would be 42 * 365 + 10 (leap years in 1968, 1972, etc.) = 15,340 days. Just like I calculated.

42 complete cycles of the sun would be 42 x the length of a year. If you use an approximation of 365.25, then you would come up with being 1/2 day off (12 hours). However, the year is *not* exactly 365.25 days long. It is closer to 365.2422 days long. To account for that we drop 3 leap years every 400 years (1900, 2100, 2200, 2300, 2500 are *not* years, but 2000, 2400, etc. *are*).

When you use 42 * 365.2422 days you get:15340.1724 days, which is about 1/6 day or 4 hours... a little more actually. I think my previous calculation is pretty close to accurate, but of course there are other factors such as the slowing of the earth because of tides, etc. that could affect the actual length of the year. I don't think the slight lengthening of the year in 42 years would affect the answer that much, but I could be wrong.