Newsgroups: sci.physics

/ hpcc01:sci.physics / ted@physics3 (Emory F. Bunn) / 10:51 pm  Aug 24, 1992 /

>>  If it is possible to resolve a person's face from a satellite, why did we
>>  spend so much money on the Hubble Telescope?
>
>   Hubble was designed to look out not in. hubble is a different animal and
>   I would suspect its capability is probably greater in terms of resolution.
>   

< Let's do the calculation.  Assume that the spy satellite is capable of
< resolving objects that are about 10 cm across.  (This is consistent
<  in order of magnitude with what Graham said, as well as what little
<  I've read on the subject.)  A typical orbital height for
< a satellite is about 3 times 10^5 meters.  So the angular size 
<  of the smallest objects the satellite can resolve is about 
<  0.1 / 3x10^5 = 3x10^-7 radians.  That's about 2x10^-5 degrees, or 
< 0.07 arc-seconds.  

<  Even taking into
<  account the fact that this is a very rough calculation, that seems
<   hard to believe.  It's significantly better than the best ground-based 
<  telescopes, which get about 0.5 arc-second resolution on a good day.  
<  Naively, one would expect those two resolutions to be comparable,
<  since they're both limited by "seeing" (atmospheric turbulence).

<  But the really fishy thing is that it's better than the resolution that
<  Hubble was supposed to get.  The Hubble was supposed
<  to be near the theoretical diffraction limit for resolution, which 
<  would be about
<  wavelength / diameter = 6 x 10^-7 meters / 1.5 meters = 
<  4 x 10-7 radians = 0.08 arc-seconds.

<  Now it seems to me that there's no way these spy satellites can get
<  around that diffraction limit, except by having a primary lens or
<  mirror that's bigger than Hubble's.  But I don't expect that they do.
<  So I think that the rough estimate of the spy-satellite resolution
<  must be overly optimistic.

<  Anybody care to comment?  Some of my numbers or calculations could
<  be wrong, or there could be some physics I'm missing.

  Well Ted you raise a good issue and one which I frankly havent thought about
  much. So last night I pulled out some of my references and took a gander. 
  I believe you are underclaiming Hubble and ground based resolution by about
  1 order of magnitude. My copy of "the New Cosmos 4th ed" by Aldrech Unsold
  gives Hubble resolution as .008 arc seconds and best ground based resolution
  as .03 arc seconds in chapter 3. Now this hubble resolution is in a different
  mode where spectrum and field of view are resricted and it sounds like some
  sort of photomultiplier is used to enhance the image brightness. 

  Also I pulled out "Deep Black" by William e. Burrows, a reading of which was
  the basis for earlier statements of a ballpark nature. Burrows is a science
  journalist, so we need to be careful, but he has covered military technology 
  etc for the NY Times, Washington Post and Wall street Journal over a 25 year
  period and is a professor of Science journalism at New York University. It
  appears that he has developed most of his info from congressional and military
  contacts (including defense contractors) and he provides 45 pages of notes
  on sources. 

  Anyway Burrows claims Keyhole 8 has about a 1 foot resolution and one of the
  later ones has 4 inch resolution. He points out that you can make out the
  windows on the russian carrier photo that graced the cover of Jane's one month  ( I looked at that issue a long time ago, right now all I can really remember
  is being impressed) It sounds like the Keyhole 8 has about an 80 inch large
  mirror and uses a configuration with a secondary mirror that increases the
  focal length beyond what would be practical for a telescope on the ground. 
  As for orbit heights, he claims keyhole 8 has about a 100 kilometer perigee
  and 300 kilometer apogee. 

  An interesting physics problem which spurred my interest in spy satellites
  is to calculate analytically the torque applied over a period to a satellite
  due to the fact that the earth is really an oblate Spheroid not a sphere. 
  (There are 2-3 problems related to this in chapter 3 of symon's mechanics
  book, note that the torque problem 3.56 has a star by it, which is deserved
  I can attest) anyway the result is that the torque depends on the angle the
  satellite makes with the equator and that the satellite will precess west 
  each revolution. A related simple problem is quantifying the advantage of
  launching east versus west. 

  Regards


Graham Flower ms 90-TT               |  Better to have convictions and act on 
Hewlett-Packard  350 W Trimble Rd    |  them, even if they are wrong, than to  
Microwave Semiconductor Division     |  waffle in indecision.
San Jose, California, 95131          |
 graham_flower@sj.hp.com             |


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