[FPSPACE] Re: FPSPACE digest, Vol 1 #137 - 5 msgs

[Robert G Kennedy III]

>Well, has we know, and by definition, an Earth day has the duration of about
>24 hours. But, in reality, an Earth day is 23 hours 56 minutes 4 seconds. In
>my database all space missions durations are with the 24 hour format. With
>so many missions now the 4 minute difference can be vey significant.

If you write the equation of motion for an earth orbiting satellite,
starting from first principles, and plug in:
- gravitational constant (or earth's grav parameter in a different formed eq)
- earth's equatorial radius,
- earth's eccentricity
- satellite inclination, and
- orbital height = perigee = apogee = ~35800 km

you will get a period of 1436 minutes plus a little bit, which is what we
expect.

Those 4 minutes per day are "lost" because, in addition to spinning like a
top, the earth is also traveling around the sun in a curved path. To a
observer fixed on earth's surface keeping time by a 24-hour clock, every
day the sun would arrive at the same precise point over the observer's head
about 4 minutes sooner that it did the day before. Multiply 365.25 x 4
minutes to see for yourself. If the orbital path were straight, i.e.
infintesimal curvature, or the period was reckoned with respect to
something really far away the galactic core (same thing) then a day really
would be 24 hours long. But 24 is divisible by many numbers which makes it
handy (base-12 math), so we use that. There are higher order corrections,
viz: leap years, centuries, etc. but that's the main one.


--
Robert Kennedy, PE
http://www.ultimax.com