Statistics – Computation
Scientific paper
Jul 1961
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1961saosr..70.....c&link_type=abstract
SAO Special Report #70 (1961)
Statistics
Computation
1
Scientific paper
The motion of Explorer 4 (Satellite 1958 Epsilon) around its center of mass is studies. This satellite body is approximated to be symmetric around its longitudinal axis, so the tangential motion can be considered a regular precession during one orbital revolution. The angular velocity vector -->ω of the body is considered to be the resultant of the precessional velocity Ψ and the angular velocity around the longitudinal axis Φ. Observations of the variations of motion, especially of Φ made during the first 60 days after launch, indicate an angular displacement of the precessional axis of at least 10° per day during the first 30 days. Also, the angular momentum of the body remained almost constant during the whole period. A method of computing the angular perturbation of the angular momentum is derived. Computations of the angular variations of the precessional axis due to atmospheric drag, using a nutation angle of 84°, yield a maximum value of 5° or 6° per day. For the gravitational torque, the same perturbation has a maximum value of 2° per day. The perturbation due to the intrinsic magnetic moment amounts to 2° per day if the maximum torque is of the order of 300 dyne cm2.The computation of the interaction of the earth's magnetic field with the shell of the body is given because it offers an explanation of the observed 10° per day angular displacement of the precessional axis. A formula is also given for computing the total perturbation per revolution, which depends on the velocity vector of the center of mass at perigee, the position of the earth's magnetic dipole related to the orbital plane, and the orbital elements. This computation is precise only for one revolution. The observed rapid decrease in Φ during the first 30 days after launch does not seem to be explained by hypothesizing the action of an external torque, since the modules of the angular momentum remained almost constant during the entire period of observation. The most probable cause of this decrease is an internal vibrational motion that causes the transfer of angular momentum from the axis of symmetry to a transverse axis. The observed variations are in good qualitative agreement with the law for the decrease in Φ.
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