From: leech@mahler.cs.unc.edu (Jon Leech)
Newsgroups: sci.space,sci.astro,news.answers
Subject: Diffs to sci.space/sci.astro Frequently Asked Questions
Date: 30 Sep 92 23:04:09 GMT
Expires: 6 Nov 92 23:04:05 GMT
Followup-To: poster
Organization: University of North Carolina, Chapel Hill
Supersedes: <diffs_715460017@cs.unc.edu>

Archive-name: space/diff

DIFFS SINCE LAST FAQ POSTING (IN POSTING ORDER)

(These are hand-edited context diffs; do not attempt to use them to patch
old copies of the FAQ).

===================================================================
diff -t -c -r1.12 FAQ.constants
*** /tmp/,RCSt1a23513	Wed Sep 30 19:02:51 1992
--- FAQ.constants	Wed Sep 30 18:59:04 1992
***************
*** 48,94 ****

	      a = 4 pi**2 r / t^2

!	  For circular Keplerian orbits, where u is gravitational constant, a is
!	      semimajor axis of orbit, P is period.
!	      v^2 = u/a
!	      P   = 2pi/(Sqrt(u/a^3))
!	      u   = G * M (can be measured much more accurately than G or M)
!
!	      Vc = sqrt(M * G / r)
!	      Vesc = sqrt(2 * M * G / r) = sqrt(2) * Vc
!	      The period of an eccentric orbit is the same as the period of a
!		 circular orbit with the same semi-major axis
!	      1/2 V**2 - G * M / r = K	(conservation of energy)
!		      where
!	      Vc   = velocity of a circular orbit (you have something like this)
	      Vesc = escape velocity
	      K    = -G * M / 2 / a
!	      M    = Mass of orbited object
!	      G    = Gravitational constant
	      r    = radius of orbit (measured from center of mass of system)
	      V    = orbital velocity

	  Change in velocity required for a plane change of angle phi in a
	  circular orbit:

	      delta V = 2 sqrt(GM/r) sin (phi/2)

!	  Energy to put mass m into a circular orbit (ignoring rotational
!	  velocity of the Earth, which reduces the energy a bit).

	      GMm (1/Re - 1/2Rcirc)
	      Re = radius of the earth
	      Rcirc = radius of the circular orbit.

!	  Classical rocket equation (dv = change in velocity, ve = exhaust
!	    velocity, x = reaction mass, m1 = rocket mass excluding reaction
!	    mass):
!
!	      dv = Ve * ln((m1 + x) / m1)
!		 = Ve * ln((final mass) / (initial mass))
!	      Ve = Isp * g = exhaust velocity, m / s
	      Isp = specific impulse of engine
!	      g = 9.80665 m / s^2

	  Relativistic rocket equation (constant acceleration)

--- 48,97 ----

	      a = 4 pi**2 r / t^2

!	  For circular Keplerian orbits where:
!	      Vc   = velocity of a circular orbit
	      Vesc = escape velocity
	      K    = -G * M / 2 / a
!	      M    = Total mass of orbiting and orbited bodies
!	      G    = Gravitational constant (defined below)
!	      u    = G * M (can be measured much more accurately than G or M)
	      r    = radius of orbit (measured from center of mass of system)
	      V    = orbital velocity
+	      P    = orbital period
+	      a    = semimajor axis of orbit

+	      Vc   = sqrt(M * G / r)
+	      Vesc = sqrt(2 * M * G / r) = sqrt(2) * Vc
+	      V^2  = u/a
+	      P    = 2 pi/(Sqrt(u/a^3))
+	      K    = 1/2 V**2 - G * M / r (conservation of energy)
+
+	      The period of an eccentric orbit is the same as the period
+		 of a circular orbit with the same semi-major axis.
+
	  Change in velocity required for a plane change of angle phi in a
	  circular orbit:

	      delta V = 2 sqrt(GM/r) sin (phi/2)

!	  Energy to put mass m into a circular orbit (ignores rotational
!	  velocity, which reduces the energy a bit).

	      GMm (1/Re - 1/2Rcirc)
	      Re = radius of the earth
	      Rcirc = radius of the circular orbit.

!	  Classical rocket equation, where
!	      dv  = change in velocity
	      Isp = specific impulse of engine
!	      Ve  = exhaust velocity
!	      x   = reaction mass
!	      m1  = rocket mass excluding reaction mass
!	      g   = 9.80665 m / s^2
!
!	      Ve  = Isp * g
!	      dv  = Ve * ln((m1 + x) / m1)
!		  = Ve * ln((final mass) / (initial mass))

	  Relativistic rocket equation (constant acceleration)