RE: Apollo 16 Saturn 4B tles guess

From: Mike McCants (mmccants@io.com)
Date: Wed May 26 2004 - 12:35:38 EDT

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    Dale Ireland asked:
    
    >First, if the Saturn
    >4B missed the Moon wasn't it heading for solar orbit.
    
    Since there were working seismic detectors on the moon from previous
    missions, many of the Saturn S4Bs were deliberately re-targeted
    to hit the moon after the CSM and LM had separated from the S4B.
    So I would assume that the timeline that says this S4B hit the moon
    is correct.
    
    In general, the tles going to the moon have a mean motion of about
    0.1 which means a 10 day orbital period.  However, the orbit is
    strongly affected by the close approach to the moon (if the S4B does
    not hit the moon), so it is difficult to generalize about what happens
    after this close approach.
    
    In particular, I ran a numerical integration of the tle that I generated
    for this mission and the close approach changed the period from 10 days
    to about 16 days.  But a couple of months after this close approach,
    there was another close approach to the moon which changed the period
    from 16 days to about 30 days.  After a year, the period was about 25 days.
    After a decade the orbit was rather circular with a period of about 50 days
    and an inclination of 77 degrees.  Many "wild swings" during that time.
    
    These are just "random numbers" since the original elset is not really
    accurate enough to predict anything.  But it illustrates that this
    kind of orbit is very unstable and that eventually such an object
    is certain to gain enough energy to escape the Earth/Moon system and
    go into solar orbit.  (Or lose enough energy to hit the Earth?)
    
    >Second, can TLE's be converted to Sun centered Keplarian elements (probably
    >first to vectors I guess) so the orbits around the Sun of other S4B boosters
    >that didn't hit the Moon can be simulated in planetarium programs?
    
    By definition, a tle is for an object that is in Earth orbit.  A tle
    for an object that is escaping Earth orbit (like a Mars probe) would
    be a "hyperbolic" orbit and have an eccentricity greater than 1.0.
    Normal satellite tracking programs could not handle such an elset.
    
    Theoretically, if you did know the orbit of such an object accurately
    enough before its encounters with the Moon, you could use a numerical
    integration program (that works with the Earth-centered vectors) to
    determine the vector as it is escaping from the Earth/Moon system.
    Then you would add the Earth's velocity vector at that time to get
    a Sun-centered vector and then you could convert that vector into
    Sun-centered orbital elements.  There is also a small problem with
    the use of the Equator for tles and the Ecliptic for solar system
    orbits.  Now we are off-topic.  :-)
    
    Moritz Heger posted:
    
    >During the Apollo missions there was measurement of at least the spacecraft
    >trajectory between earth and moon by Doppler radar. I would suggest to look
    >for such data first when one wants to calculate solar orbits of debris
    >stages. I do not know if the Horizons Ephemeris System gives this data for
    >Apollo stages.
    
    But the S4B was deliberately re-targeted to be away from the spacecraft.
    I assume that the S4B had batteries only and could not be tracked after
    a few more hours.
    
    j smith posted:
    
    >For the Apollo 16 Saturn booster that impacted the Moon, from the Apollo 16
    >Saturn V launch vehicle report AS-511, pg 17-5 (lunar impact section)....
    >
    >Geocentric Orbit Parameters following APS Impact Burn
    ..
    >Other stuff available if useful.
    
    Interesting, but this is not enough information to determine the actual
    tle or velocity vector.  At any rate, by the time such an object was
    actually ejected from the Earth/Moon system some months later, the
    orbit would not be accurate unless there was some tracking during the
    time it was in its "loosely-bound" Earth orbit.  (IMO)
    
    Mike McCants
    
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