From: roberts@cmr.ncsl.nist.gov (John Roberts)
Subject: Mascons
X-Added: Forwarded by Space Digest
Organization: National Institute of Standards and Technology formerly National Bureau of Standards
Original-Sender: isu@VACATION.VENARI.CS.CMU.EDU
Distribution: sci
Date: Sat, 7 Nov 1992 01:46:58 GMT


-From: gary@ke4zv.uucp (Gary Coffman)
-Subject: Re: NASA Coverup
-Date: 6 Nov 92 16:49:19 GMT
-Organization: Gannett Technologies Group

-In article <4592@cruzio.santa-cruz.ca.us> snarfy@cruzio.santa-cruz.ca.us writes:
->   Beiser states , on page 118 , "A spherical object behaves  gravitationally
->   as  if  it's  mass  were concentrated at it's center" . He also states,on
             ----                             ----

Beiser doesn't have a very good proofreader, does he? :-)

->   page 119, that  the  earth's  gravitational  pull  on  an  object  varies
->   inversely  with the square of it's distance FROM THE CENTER OF THE EARTH.
->   I also assume that a similar rule applies to the moon.

-It doesn't even apply to the Earth. One of the things learned from early
-satellite launches is that the Earth, and to an even greater extent the
-Moon, have what are called mascons, mass concentrations. These are unevenly
-distributed areas of higher density inside the body. Beiser's assumption
-holds up as a close approximation when the two bodies are far enough 
-apart that their radius is an insignificant part of their separation
-distance, say Earth-Sun distance. But they fail miserably when the
-separation is less than a few body radiuses. The mascons will warp the
-orbit of the satellite a measurable amount. 

The moon has both positive (filled crater) and negative (unfilled crater)
surface mascons that perturb its gravitational field to such an extent that
an object in low lunar orbit is essentially guaranteed to crash into the
moon fairly quickly. The Earth, being a geologically active planet, is in
isostatic equillibrium, so that an object in even a 200-mile circular orbit
will retain pretty much the same orbit until atmospheric drag gets it. The
Lageos satellites (one just launched on the latest Shuttle mission), orbiting
at about one Earth radius above the surface, are expected to remain there
for about eight *million* years (and being passive reflectors, they should
continue to be usable "indefinitely"). The Earth does have an equatorial
bulge (mentioned later in your post), which is caused by the rotation of the
planet, which I believe has the main effect of perturbing the ascending node
of high-inclination orbits. This is what makes sun synchronous orbits
possible, and since Mars Observer is scheduled to take up a sun synchronous
orbit, I presume Mars has a similar equatorial bulge.

-The existance of tides is a direct result of the effect
-of differentials in gravitational potential across the diameter of a 
-body. Using Beiser's simplifing assumption, there could be no tides on
-Earth. Since we can easily observe that there are, his assumption is
-invalid for bodies as close together as the Earth and the Moon.

That's a little bit misleading - a point-source moon would still cause
tides on the Earth. I don't have any idea whether the fact that the moon
is a distributed mass has any significant influence on the magnitude of the
tides.

John Roberts
roberts@cmr.ncsl.nist.gov

Newsgroups: sci.space