Question

the position of a planet orbiting the sun is described by the coordinates x and y draw a graph showing the variation of the areal velocity of the Planet with the co-ordinate x​

Answer 1

Answer:

Since areal velocity is constant so the graph of areal velocity will be a straight line parallel to x axis

Explanation:

As we know that planet will experience force due to gravitational force of Sun

this force is given as

$F = \frac{GM_sm_p}{r^2}$

now this force is always towards the sun

Now if we take reference on the position of Sun then torque at the position of planet with respect to Sun is always ZERO

so we will have

$\frac{dL}{dt} = \tau = 0$

so the angular momentum of the planet will remain conserved

Now for areal velocity of Sun

$dA = \frac{1}{2}r^2 d\theta$

now rate of change in area is given as

$\frac{dA}{dt} = \frac{1}{2}r^2\frac{d\theta}{dt}$

$\frac{dA}{dt} = \frac{1}[2m}(mr^2 \omega)$

$\frac{dA}{dt} = \frac{L}{2m}$

So here areal velocity of the planet will remain constant always

#Learn

Topic : Kepler's law

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