Re: An elementary, but puzzling question

From: Rick Brown (rbrown@inetnebr.com)
Date: Sat May 20 2000 - 16:27:03 PDT

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    Hi Roger--
    
    The short answer to why a satellite crosses the equator twice is that gravity
    is always pulling it toward the center of the earth.
    
    But here's a somewhat longer answer :-)
    
    Picture in your mind the orbit of a satellite.  The laws of physics say the
    orbit must be shaped like an ellipse (roughly, an oval), which is a flat shape
    and which therefore lies on a plane (the plane may be tilted relative to the
    equator, but it's still a plane).
    
    So picture the plane on which the orbital ellipse lies, and imagine that plane
    as it slices through the earth.  For the sake of argument, let's pretend that
    the orbit always stays over the same latitude (say the latitude of KSC); this
    means the orbital plane would slice the earth into two unequal pieces; the
    "southern" piece being larger than the "northern" piece.
    
    But here's the problem: the laws of physics say that the center of the earth
    must be contained within any orbital plane.  The reason for this has to do
    with the fact that the pull of gravity is always toward that point at the
    earth's center; any object responding to a force directed toward a single
    point will always move in a plane that contains that point. 
    
    But if you think about the plane of our hypothetical "KSC latitude" orbit,
    which sliced the earth into a small northern piece and a larger southern
    piece, you'll see that that plane definitely does _not_ contain the earth's
    center.  In order for a plane to contain the earth's center, it must slice the
    earth into two _equal_ halves.
    
    This means it's impossible for any orbit to remain always in the northern
    hemisphere.  A similar argument shows it's also impossible for any orbit to
    remain always in the _southern_ hemisphere.
    
    And that leaves us with just two possibilities: either your orbit must remain
    directly over the equator at all times, or it must cross into both hemispheres
    during each orbit.  Orbits of the second kind are probably more common, and
    they cross the equator twice during each orbit; once northbound and once southbound.
    
    Hope this makes it a little clearer for you.  (I have made some
    simplifications about the geometry of the earth and the forces acting on
    satellites which are not strictly accurate, but they're close enough to get
    the general idea across.)
    
    - Rick Brown
    
    Roger Curry wrote:
    > 
    > >From the point of view of a satellite, it is following a straight
    > path around the Earth, but from the point of view of the
    > ground, it crosses the equator twice during each orbit
    > and reaches a northern and southern latitude equal to the
    > angle it crosses the equator.
    > 
    > When a rocket is launched from, say, KSC, is it programmed
    > to fly south of east so that it crosses the equator somewhere
    > over Africa if it is in a 28.5 deg. inclination orbit, or does it just
    > travel east and somehow the axial tilt of the Earth does the
    > job of making it cross the equator twice?  I have used a pencil
    > held just above a rotating globe at the latitude of KSC and
    > it remains at the same latitude all the way around.
    > 
    > Thanks for any elucidation, and I hope the answer is not so
    > obvious that people will be saying, "Duh!".
    > 
    > Clear skies.
    > 
    > Roger in Jacksonville, FL.
    > Nice view of the shuttle launch here this morning, BTW!
    > 
    > ---------------
    > Roger Curry
    > Jacksonville, Florida
    > Visit the NEFAS Web Site at www.nefas.org
    > Roger's FTP site:  ftp://24.129.70.60
    > 
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