If A is a real velocity of a planet mass M, then its angular momentum is nMA, where n is what?

Question:

If A is a real velocity of a planet mass M, then its angular momentum is nMA, where n is what?

Kepler's planetary law:

Angular momentum is equivalent to linear momentum in rotational motion. Angular momentum is also conserved quantity as linear momentum. The angular momentum is the cross product of position vector and linear momentum.

Kepler's planetary law:

After Failure of heliocentric model suggested by Nicolas Copernicus, the planetary motion was explained by the three laws suggested by Kepler.

  • Planets moves around Sun in an elliptical path, with Sun present at its one of the foci
  • Sun and the planet are joined by the line segment, which sweeps out equal area in equal time.
  • The square of the planetary orbital period is proportional to the cube of the semi-major axis of its orbit.

Answer and Explanation:

Given,

Mass of the planet, {eq}\rm M {/eq}

Velocity of planet, {eq}\rm A {/eq}

Angular momentum, {eq}\rm L=nMA {/eq}

Calculation:

According to Kepler's second law of planetary motion we have,

{eq}\rm \dfrac{dx}{dt} = \dfrac{L}{2M} {/eq} ...(1)

Where,

{eq}\rm L {/eq}= Angular momentum

Thus, velocity of the planet is given by,

{eq}\rm A = \dfrac{dx}{dt} {/eq}

Substituting the value of velocity in equation (1), we get

{eq}\rm A= \dfrac{L}{2M} {/eq}

{eq}\rm L=2MA {/eq}

Comparing with given value of angular momentum we get,

{eq}n = 2 {/eq}


Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
46K

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