Answer to Question #159734 in Classical Mechanics for afiqah

Question

Motion of a planet of mass mp in our solar system is an example of motions under the action of

central force ⃗F

c due to the sun of mass Ms.

a) Is ⃗Fc a conservative force? Explain your answer.

b) It is well known that the planet is moving about the sun in a same fixed orbit located on a

fixed orbital plane. Name two (2) physical principles that dictate why the planet moves the

way it does. Explain your answers.

c) The orbit of the planet has an eccentricity ϵ = 0.047 and semi-major axis a = 19.18 AU. Use

the octave script provided to plot the orbit. Mark the perihelion and the aphelion centre of

the orbit on the plot.

Answer 1

Any force is a conservative force if the work done by the force in moving a particle between two points is independent of the path.

Here work done by the force is also independent, so here $\tau$ force is conservative force.

b) If any massive object is moving in the circular orbit, then it must have the centripetal force, here planet have have the considerable mass and it is moving in the circular orbit, so it must have the centripetal force other is gravitational force between the planet and sun.

$\Rightarrow \frac{mv^2}{R}=\frac{GmM}{R^2}$

$\Rightarrow v= \sqrt{\frac{GM}{R}}$

c)$b=a(1-e^2)^{1/2}$

$\Rightarrow b=19.18(1-0.047^2)^{1/2}AU$

$\Rightarrow b=19.15AU$