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According to Kepler, the period of revol...

According to Kepler, the period of revolution of a planet ( T ) and its mean distance from the sun ( r ) are related by the equation

A

`T^(3)r^(3)=` constant

B

`T^(2)r^(-3)=` constant

C

`Tr^(3)=` constant

D

`T^(2) r=` constant

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • Planets and comets follow an elliptical path around the Sun, with the Sun lying at one of the foci of the ellipise. This motion is due to the gravitational force of attraction acting between the Sun and the planets (or comets), which is central in nature. This further implies that the angular momentum of a planet moving around the Sun is constant. When a planet is nearer the Sun, it speeds up while it slows down when it is farther away. One could also predict the time period (T) of revolution of a planet from a knowledge of its mean distance (R ) from the Sun i.e., the average of its distances from the Sun at aphellon (farthest point) and perihelion (nearest point), since T^(2) prop R^(3) This equation is also valid for circular orbits and the constant of proportionality is the same for both. A comet of mass m moves around the Sun in closed orbit which takes it to a distance of a when it is closest to the Sun and a distance of 4a when it is farthest from the Sun. Assume that the mass of the Sun is M . The gravitational potential energyof the comet varies from the aphelion to the perihelion during the course of its revolution. The maximum variation in its kinetic energy is (KE_(max)-KE_(min))

    A
    `(3GMm)/(a)`
    B
    `(5GMm)/(a)`
    C
    `(GMm)/(a)`
    D
    none of the above

  • Planets and comets follow an elliptical path around the Sun, with the Sun lying at one of the foci of the ellipise. This motion is due to the gravitational force of attraction acting between the Sun and the planets (or comets), which is central in nature. This further implies that the angular momentum of a planet moving around the Sun is constant. When a planet is nearer the Sun, it speeds up while it slows down when it is farther away. One could also predict the time period (T) of revolution of a planet from a knowledge of its mean distance (R ) from the Sun i.e., the average of its distances from the Sun at aphellon (farthest point) and perihelion (nearest point), since T^(2) prop R^(3) This equation is also valid for circular orbits and the constant of proportionality is the same for both. A comet of mass m moves around the Sun in closed orbit which takes it to a distance of a when it is closest to the Sun and a distance of 4a when it is farthest from the Sun. Assume that the mass of the Sun is M . It is observed that the total energy ( KE+ gravitational PE ) is conserved. The toal energy of the comet is

    A
    `-(3GMm)/(4a)`
    B
    `-(3GMm)/(8a)`
    C
    `-(GMm)/(5a)`
    D
    none of these

  • According the Kepler's law, the areal velocity of a planet around the sun, always

    A
    increases
    B
    decreases
    C
    remains constant
    D
    first increases and then decreases

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