Kepler's Orbits A particle of mass p moves with angular momentum l inthe field of a fixed force center withkF(r) =+r3r 2where k and A are positive constants.(a) Applying the radial differential equation uř = F(r) +l2/(ur3) to derive a transformedradial differential equation for u(), where u = 1/r.(b) Prove that the orbit has the formtle from the separationсr(o)1+E cos (B)and find c and B in terms of the given parameters.Hint: It is helpful to review the derivation we did in class for the case F(r) = -7/r2.

Question
Asked Nov 26, 2019
104 views
Kepler's Orbits A particle of mass p moves with angular momentum l in
the field of a fixed force center with
k
F(r) =
+
r3
r 2
where k and A are positive constants.
(a) Applying the radial differential equation uř = F(r) +l2/(ur3) to derive a transformed
radial differential equation for u(), where u = 1/r.
(b) Prove that the orbit has the form
tle from the separation
с
r(o)
1+E cos (B)
and find c and B in terms of the given parameters.
Hint: It is helpful to review the derivation we did in class for the case F(r) = -7/r2.
help_outline

Image Transcriptionclose

Kepler's Orbits A particle of mass p moves with angular momentum l in the field of a fixed force center with k F(r) = + r3 r 2 where k and A are positive constants. (a) Applying the radial differential equation uř = F(r) +l2/(ur3) to derive a transformed radial differential equation for u(), where u = 1/r. (b) Prove that the orbit has the form tle from the separation с r(o) 1+E cos (B) and find c and B in terms of the given parameters. Hint: It is helpful to review the derivation we did in class for the case F(r) = -7/r2.

fullscreen
check_circle

Expert Answer

Step 1

(a) Using the given radial differential equation, the force in terms of u is,

help_outline

Image Transcriptionclose

=-ku2 + Au? +

fullscreen
Step 2

Transforming the differentials from r to u,

help_outline

Image Transcriptionclose

drdo dt dt dou 1 du do du m do

fullscreen
Step 3

Moreover...

help_outline

Image Transcriptionclose

dr do 1l du dt dt dou do μ dφ -Pu d°u

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.

Related Advanced Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add