In an elliptical orbit under gravitational force, in general

(a) Tangential velocity is constant

(b) Angular velocity is constant

(c) Radial velocity is constant

(d) Areal velocity is constant

Concept Questions :-

Kepler laws
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Earth is revolving around the sun, if the distance of the Earth from the Sun is reduced to 1/4th of the present distance then the present year length reduced to -

(a)$\frac{1}{4}$                                         (b)$\frac{1}{2}$

(c)$\frac{1}{8}$                                         (d)$\frac{1}{6}$

Concept Questions :-

Kepler laws
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Two satellite are revolving around the earth with velocities ${v}_{1}$ and ${v}_{2}$ and in radii ${r}_{1}$ and ${r}_{2}\left({r}_{1}>{r}_{2}\right)$respectively. Then -

(a)${v}_{1}={v}_{2}$                                 (b)${v}_{1}>{v}_{2}$

(c)${v}_{1}<{v}_{2}$                                 (d)$\frac{{v}_{1}}{{r}_{1}}=\frac{{v}_{2}}{{r}_{2}}$

Concept Questions :-

Orbital velocity
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If orbital velocity of planet is given by $v={G}^{a}{M}^{b}{R}^{c}$, then -

(a)

(b)

(c)

(d)

Concept Questions :-

Orbital velocity
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The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as -

(a)$4{\mathrm{\pi }}^{2}{\mathrm{R}}^{3}{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$                                 (b)$8{\mathrm{\pi }}^{2}{\mathrm{R}}^{3}{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$

(c)$12{\mathrm{\pi }}^{2}{\mathrm{R}}^{3}{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$                               (d)$16{\mathrm{\pi }}^{2}{\mathrm{R}}^{3}{\mathrm{G}}^{‐1}{\mathrm{T}}^{‐2}$

Concept Questions :-

Satellite
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The eccentricity of earth's orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is

(a)   2.507                                             (b)   1.033

(c)   8.324                                             (d)   1.000

Concept Questions :-

Kepler laws
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Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth -

Concept Questions :-

Acceleration due to gravity
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The radius of orbit of a planet is two times that of the earth. The time period of planet is -

(a)   4.2 years                           (b)   2.8 years

(c)   5.6 years                           (d)   8.4 years

Concept Questions :-

Kepler laws
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The diagram showing the variation of gravitational potential of earth with distance r from the centre of earth is -

Concept Questions :-

Gravitational Potential
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The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be -

(a)   16 L                                   (b)   64 L

(c)    $\frac{L}{4}$                                     (d)   4 L

Concept Questions :-

Orbital velocity
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