Newton's Era Fundamental Framework Present Theories Exercise Gallery
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 LAWS OF MOTION

From here, we get a proof of Kepler’s area law.

Consider the figure:

For small q, OAB can be called a triangle. Now area of DOAB=(1/2)r2sindq.
Since d
q is very small, sinddq. Therefore, small area dA=(1/2)r2dq.

From (1), we have,

We get the area on integrating.

For ellipse law, assume the Newton’s inverse square law.

 Acceleration=-GM/r2. This acceleration is

(the acceleration due to change in radius and due to rotational motion).

Since w = dq/dt,
we have,

....(2)

Using Relation (1),

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