A planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct ?

823-1441

  • A

    $\frac{{{r_P}}}{{{r_A}}} = \frac{{{v_A}}}{{{v_P}}}$

  • B

    $\frac{{{r_P}}}{{{r_A}}} = \frac{{{v_P}}}{{{v_A}}}$

  • C

    $\frac{{{r_P}}}{{{r_A}}} = \sqrt {\frac{{{v_P}}}{{{v_A}}}} $

  • D

    $\frac{{{r_P}}}{{{r_A}}} = \sqrt {\frac{{{v_A}}}{{{v_P}}}} $

Similar Questions

$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.

A spherical planet far out in space has a mass ${M_0}$ and diameter ${D_0}$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

If the radius of the earth were shrink by $1\%$ and its mass remaining the same, the acceleration due to gravity on the earth's surface would

Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre ofthe planet for $r \ge $ radius of the planet. Plots $1$ and $2$ coincide for $r \ge {R_2}$ and plots $3$ and $4$ coincide for $r \ge {R_4}$ . The sequence of the planets in the descending order of their densities is

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is