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Impact parameters between a pair of objects

 The Figure shows the passage of a solar wind phase plane over a pair of spacecraft. The phase plane is shown as normal to the ecliptic and intersecting the ecliptic (X-Y) plane at an angle midway between the Parker spiral angle (shown with the B vector) and the Y axis. The solar wind is carrying the phase plane with speed V in the -X direction. The inertial coordinate system is coincident with Geocentric Solar Ecliptic at time t0. Time t0 is defined as the time the phase plane sweeps over the spacecraft labelled ACE. Time t1 is defined as the time the plasma element observed by ACE at time t0 reaches the X coordinate of the spacecraft labelled Wind; t1 is the time when the distance between Wind and the plasma element is minimized. Between t0 and t1, Wind shares in Earth's ~30 km/s circumsolar motion (which is much larger than Wind's motion relative to the Earth.). Geometrically, the Impact Parameter, shown as IP in the figure, is the length of the Y-Z-plane projection of the vector joining ACE at t0 and Wind at t1. Physically, IP is the minimum distance experienced between Wind moving at 30 km/s in Y and the plasma element moving at 390 km/s in X.

We have used a value of 390 km/s for solar wind speed (V) in our computations of impact parameter. Of course the solar wind flow speed is variable, so our impact parameter values are only approximations to the real values for any time and spacecraft pair. Over the full solar activity cycle 1990-2000, the average solar wind speed is 433 km/s, the median is 408 km/s and the most probable value lies in the 370-380 km/s range. These numbers are larger (smaller) for the solar active (quiet) year 1999 (1995). Thus 390 km/s is somewhat "typical." Using a higher assumed flow speed for our calculations would have led to smaller or larger impact parameter values according to the sign of the difference of Y components of spacecraft position vectors.

Note: Regrettably, the text accompanying this figure in the King and Papitashvili paper of the February, 2005, JGR - Space Physics issue incorrectly associates time t1 with the passage of the phase plane over the Wind spacecraft.

 If you have any questions/comments about the FTPWeb Browswer, contact: Dr. Natalia Papitashvili, Mail Code 672, NASA/Goddard Space Flight Center, Greenbelt, MD 20771