The figure shows elliptical orbit of a planet m about the sun s. the shaded area SCD is twice th

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The figure shows elliptical orbit of a planet m about the...

The figure shows elliptical orbit of a planet $\mathrm{m}$ about the sun s. the shaded area $\mathrm{SCD}$ is twice the shaded area $\mathrm{SAB}$. If $\mathrm{t}_{1}$ is the time for the planet to move from $\mathrm{C}$ and $\mathrm{D}$ and $\mathrm{t}_{2}$ is the time to move from $\mathrm{A}$ to $\mathrm{B}$ then

The figure shows elliptical orbit of a planet $\mathrm{m}$ about the sun
s. the shaded area $\mathrm{SCD}$ is twice the shaded area $\mathrm{SAB}$. If $\mathrm{t}_{1}$ is the time for the planet to move from $\mathrm{C}$ and $\mathrm{D}$ and $\mathrm{t}_{2}$ is the time to move from $\mathrm{A}$ to $\mathrm{B}$ then

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Key Concepts

Areal Velocity

Areal velocity is the measure of the rate at which area is swept by the line connecting a planet to the sun. Because this rate is constant for a body under a central force, it creates a direct proportionality between the time spent in a given orbital segment and the area of that segment.

Elliptical Orbits

Elliptical orbits describe the path of a planet around the sun, with the sun located at one of the foci of the ellipse. The geometric properties of ellipses, combined with the conservation of angular momentum, lead to variations in the planet's speed along its orbit while ensuring that the area swept per unit time remains constant.

Kepler's Second Law

Kepler's Second Law states that a line joining a planet and the sun sweeps out equal areas during equal intervals of time. This means the areal velocity of a planet in its orbit remains constant, which directly relates the time taken to traverse any section of the orbit to the area swept out, regardless of the orbital speed at different points.

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