|Re: How much accuracy does one actually need?|
Message #8 Posted by htom trites jr on 24 Aug 2013, 9:26 p.m.,
in response to message #1 by Matt Agajanian
Depends. Circumference of the Milky Way Galaxy is about 1.75e24 meters (120,000,000 light year diameter), so slight errors may put you in the wrong parking place on the opposite edge unless you're careful in your cross-galaxy navigation. Remember to compensate for motions while you travel.
Earth or Solar System bound, you can probably get by with five decimal digits.
The problem really comes along when you compare two numbers and make decisions on the noise after those five digits. That's when you need the high accuracy calculations.
Finance counts by the penny, and with budgets in the billions, fourteen or fifteen decimal digits (assuming the bankers are smart enough to use integer pennys) can suffice. So far.
=== edit for error check. perhaps km for m error?
120,000,000 ly diameter / 2 = 60,000,000 ly radius
60,000,000 ly * pi = 188,495,559.215 ly circumference /free42/
188,495,559.215 ly * 365.25 = 68,848,003,003.4 ldays
68,848,003,003.4 ldays * 24 * 60 * 60 = 5.9484674595e14 seconds
5.9484674595e14 seconds * 299,792,458 m/s = 1.78330568102e23 meters
oops. wait. Diameter, not radius, so double that result,
Solar System diameter ~9e12 meters
Finding the parking space is still a problem. You might miss the Solar System!
Edited: 25 Aug 2013, 1:11 a.m. after one or more responses were posted