On Sat, 11 Jul 2015 15:02:41 -0400, Phil Hobbs
wrote:
The fun starts when tracking spacecraft in otter space. Not only does
one have to deal with relativistic effects, but one also has to use a
time system that is independent of how the earth spins, wobbles, and
thrashes around. It would be a major disaster if a leap second were
thrown into the timing if you're tracking a spacecraft such as Voyager
1 moving at 17 km/sec (38,000 mph).
You'd be off by 17 km. Is Voyager 1's position known to that accuracy?
Didn't think so.
I was thinking of it in terms of the change in angular error for the
rotation of the earth.
degrees = 17km/40,075km * 360 degrees = 0.15 degrees
Let's see if that works. Voyager 1 and 2 uses the DSN (deep space
network) with 34 or 70 meter dishes at about 8 GHz. That's about 67dB
gain and a -3db beamwidth of about 0.07 degrees for the 34 meter dish,
and 73 db gain and 0.04 degree beamwidth for the 70 meter dish. Since
the DSN tracks the rotation of the earth, a change of 0.15 degrees
would move the main lobe sufficiently to miss the spacecraft.
http://www.satsig.net/pointing/antenna-beamwidth-calculator.htm
http://www.uhf-satcom.com/misc/datasheet/dh2va.pdf
Maybe so, if they'd lost their minds and were using their computer
clocks to aim the DSN, but that's a fantasy. Orbital mechanics bods are
all over this timekeeping stuff. It's the stupid software developers
who don't know or don't care.
Digging deeper. See:
http://descanso.jpl.nasa.gov/performmetrics/DSN_NavSysAccuracy.pdf
http://descanso.jpl.nasa.gov/performmetrics/perfmetric.html
It shows the current DSN aiming accuracy at 0.1 nanorads or 15 meters
at 1 AU distance. Voyager 1 is currently at 131 AU distance:
http://voyager.jpl.nasa.gov/where/
That grinds out to an accuracy of 2 km meters at a range of 19.6
billion km. Yes, NASA does know the position of Voyager 1 to less
than 17 km.
Incidentally, that an angular resolution of:
arctan(2/19.6*10^9) = 0.000000006 degrees (or 6*10^-9 deg)
A 0.15 degree error, caused by a leap second, would produce a rather
astronomical pointing error.
Wow, that's impressive (or I mangled the math again).
--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060
http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558