"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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33ac7d32-eb4d-4de3-9195-156cd423b255%2F59403e41-a38b-42c1-a5bd-33be5c31c476%2F2vmq2y_processed.png&w=3840&q=75)
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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