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"Interstellar bullets" are thought to be thick clumps of gas which move like ballistic particles through lower-density interstellar gas clouds. Consider a uniform circular cloud of sweep R, mass M, and a "bullet" of radius « R and mass m « M. Overlook all non-gravitational intelligent. (a) Get expressions for the constrain F(r), 0

"Interstellar bullets" are thought to be thick clumps of gas which move like ballistic particles through lower-density interstellar gas clouds. Consider a uniform circular cloud of sweep R, mass M, and a "bullet" of radius « R and mass m « M. Overlook all non-gravitational intelligent. (a) Get expressions for the constrain F(r), 0

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"Interstellar bullets" are thought to be thick clumps of gas which move like ballistic particles through lower-density interstellar gas clouds. Consider a uniform circular cloud of sweep R, mass M, and a "bullet" of radius « R and mass m « M. 0verlook all non-gravitational intelligent. (a) Get expressions for the constrain F(r), 0 < r < o, endured by the bullet in terms of the remove r from the cloud center, and for the potential energy V(r), 0 <r < o. Outline V(r). (b) The bullet has precise energy L = m(GMR/32)^.5 approximately r = 0 and add up to vitality E = -5GMM/4R. Discover the circle turning point(s). Is the bullet continuously within the cloud, exterior the cloud, or some of the time interior and sometimes outside? (c) For L and E as in (b), get an expression for the differential orbit angle de in terms of dr, r and R. (d) Get an circle condition r(0, R) by coordination your reply to (c), you may wish to utilize da -2cx – b Va + bx + cx2 arcsin V – 4ac' c < 0. Find the turning points r1 and sketch the orbit. 64
Transcribed Image Text:"Interstellar bullets" are thought to be thick clumps of gas which move like ballistic particles through lower-density interstellar gas clouds. Consider a uniform circular cloud of sweep R, mass M, and a "bullet" of radius « R and mass m « M. 0verlook all non-gravitational intelligent. (a) Get expressions for the constrain F(r), 0 < r < o, endured by the bullet in terms of the remove r from the cloud center, and for the potential energy V(r), 0 <r < o. Outline V(r). (b) The bullet has precise energy L = m(GMR/32)^.5 approximately r = 0 and add up to vitality E = -5GMM/4R. Discover the circle turning point(s). Is the bullet continuously within the cloud, exterior the cloud, or some of the time interior and sometimes outside? (c) For L and E as in (b), get an expression for the differential orbit angle de in terms of dr, r and R. (d) Get an circle condition r(0, R) by coordination your reply to (c), you may wish to utilize da -2cx – b Va + bx + cx2 arcsin V – 4ac' c < 0. Find the turning points r1 and sketch the orbit. 64
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