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Q: Seconds in a year ( Answered,   3 Comments )
Subject: Seconds in a year
Category: Science > Physics
Asked by: freckles1000-ga
List Price: $2.00
Posted: 28 Aug 2003 19:16 PDT
Expires: 27 Sep 2003 19:16 PDT
Question ID: 250025
The astronomical basis of our calendar year is the tropical year, from
the solar position of a vernal equinox to the position of the next
vernal equinox.  This year contains 365.242199 days.  How many seconds
are in this year(2003)?
Subject: Re: Seconds in a year
Answered By: robertskelton-ga on 28 Aug 2003 19:46 PDT
Hi there,

A day has 24 hours x 60 minutes x 60 seconds = 86,400 seconds per day.

365 x 86,400 = 31,536,000 seconds

All we have to do is add how many seconds are in .242199 days...

86,400 times .242199 = 20,925.9936

+   20,925.9936

There are 31,446,925.9936 seconds in a topical year in 2003.

The topical year only changes by about half a second every century, so
that answer will be accurate to one second for many years to come.

Best wishes,

Clarification of Answer by robertskelton-ga on 28 Aug 2003 19:48 PDT
Oops, see what happens when I don't use Google to make the calculation!

It should read:

There are 31,556,925.9936 seconds in a topical year in 2003.

Clarification of Answer by robertskelton-ga on 28 Aug 2003 19:49 PDT
The number I arrived at also appears within this document:
Subject: Re: Seconds in a year
From: cev-ga on 08 Sep 2003 14:47 PDT
This is an easy rule-of-thumb: there are pi x 10^7 seconds in a year.
Subject: Re: Seconds in a year
From: scidan-ga on 29 Apr 2004 13:42 PDT
> ... rule-of-thumb ... 
Yes, give and take 0,5%...
Subject: Re: Seconds in a year
From: ranslow-ga on 09 Jun 2004 16:03 PDT
I'm not sure how you are coming to the conclusion that there are pi x
10^7 seconds in a year.

This hardly seems grounded on anything. 
    31,556,925.9936                     (Calculated by other means)
    31,415,926.535897932384626433832795 (pi * 10^7)

When you approximate the number of seconds in a year you can look it as
    [number of days in year] * [seconds in a day]

or you can:
Calculate the circumference of the earth's orbit and divide by the
speed of the earth's rotation.  Like this:
Radius of Earth's Orbit (r) = (1) Astronomical Unit

circumference = 2*r*pi
2*1*pi = 6.283185307179586476925286766559 (The circumference = 6.28 AUs)

An AU is approximated by 149,600,000 km

convert AUs to km by multiplying (6.283185307179586476925286766559 * 149600000)
   = 939964521.95406613694802290027723

The earth's speed is estimated to be 29.7859 km/s

The number of seconds in a year equals:
circumference / Earths_speed
939964521.95406613694802290027723 / 29.7859 = (31557365.127596149082217522394059)

  The number of seconds = (31557365.127596149082217522394059)

This is another dandy estimate.  However the solution is only as good
as the samples that support it.
(see )

Indeed there are better ways like actually calculating the
circumference of the ellipse that the earth's orbit is.

But then we are still limited by the estimates given by samples (or
other calculations).  Otherwise we are caught in a case of
merrygoround mathematics. By this I mean if the speed of Earth
determined by using the circumference then how do we know what the
circumference is.  And if the circumference is determined by using the
speed then how fast is the Earth traveling.

Clearly we need a better way of determining how many seconds are in a year.

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