MOTION MOUNTAIN

338 a units, measurements and constants
TA B L E 29 (Continued) Astronomical constants.
Quantity Symbol Value
againstcosmicbackground
Sun’ssurfacegravity g⊙ 274 m/s 2
Sun’slowerphotosphericpressure p⊙ 15 kPa
DistancetoMilkyWay’scentre 8.0(5) kpc=26.1(1.6) kal
MilkyWay’sage 13.6 Ga
MilkyWay’ssize
c.10 21 mor100 kal
MilkyWay’smass 10 12 solarmasses,c.2⋅10 42 kg
Mostdistantgalaxy clusterknown SXDF-XCLJ 9.6⋅10 9 al
0218-0510
Challenge 331 s
Ref. 299
Challenge 332 s
a. Defining constant, from vernal equinox to vernal equinox; it was once used to define the
second. (Remember:πseconds is about a nanocentury.) The value for 1990 is about0.7 s less,
correspondingtoaslowdownofroughly0.2 ms/a.(Watchout:why?) Thereisevenanempirical
formula forthechangeofthelength oftheyearovertime.
b.ThetrulyamazingprecisionintheaveragedistanceEarth–Sunofonly30 mresultsfromtime
averagesofsignalssentfromVikingorbitersandMarslanderstakenoveraperiodofovertwenty
years.NotethattheInternationalAstronomicalUniondistinguishestheaveragedistanceEarth–
Sun from the astronomical unit itself; the latter is defined as a fixed and exact length. Also the
light year is a unit defined as an exact number by the IAU. For more details, see www.iau.org/
public/measuring.
c. The shapeof the Earth is described most precisely with the World Geodetic System. The last
edition dates from 1984.For an extensive presentationof its background and its details, see the
www.wgs84.comwebsite.The InternationalGeodesicUnionrefined thedata in2000. The radii
andtheflatteninggiven hereare thoseforthe ‘mean tidesystem’.They differfromthoseof the
‘zerotidesystem’ andothersystemsbyabout0.7 m.Thedetails constituteascienceinitself.
d. Measured centre to centre. To find the precise position of the Moon at a given date, see
the www.fourmilab.ch/earthview/moon_ap_per.html page. For the planets, see the page www.
fourmilab.ch/solar/solar.htmlandtheotherpagesonthesamesite.
e.Anglesaredefinedasfollows:1degree=1 ∘ =π/180rad,1(first)minute=1 =1°/60,1second
(minute)=1 =1 /60.Theancientunits‘thirdminute’ and ‘fourthminute’,each1/60thofthe
preceding, are not in use any more. (‘Minute’ originally means ‘very small’, as it still does in
modernEnglish.)
Some properties of nature at large are listed in the following table. (If you want a challenge,canyoudeterminewhetheranypropertyoftheuniverse
itself is listed?)
TA B L E 30 Cosmological constants.
Quantity Symbol Value
Cosmologicalconstant Λ c.1⋅10 −52 m −2
Ageoftheuniverse a t 0 4.333(53)⋅10 17 s=13.8(0.1)⋅10 9 a
(determined fromspace-time,viaexpansion,usinggeneralrelativity)
Ageoftheuniverse a t 0 over3.5(4)⋅10 17 s=11.5(1.5)⋅10 9 a
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net