408 Universal Gravitation*P13.67Let mrepresent the mass of the meteoroid and viits speed when far away.No torque acts on the meteoroid, so its angular momentum is conserved asit moves between the distant point and the point where it grazes the Earth,moving perpendicular to the radius:FIG. P13.67LLif=:mmiiffrvr v×= ×mRv mRvvvEiE ffi33bg==Now energy of the meteoroid-Earth system is also conserved:KUgigf+=+ej:1201222mvmvGM mREE−12129GMREE=−GMRvEEi=42:vGMRiEE=4*P13.68From Kepler’s third law, minimum period means minimum orbit size. The “treetop satellite” inFigure P13.35 has minimum period. The radius of the satellite’s circular orbit is essentially equal tothe radius Rof the planet.Fma∑=:GMmRmvRmRRT2222==FHGIKJπGV
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .