A satellite S is moving in an elliptical orbit around earth. mass of satellite is very small compare

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7.Gravitation

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A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

the acceleration of $S$ is always directed towards the centre of the earth

the angular momentum of $S$ about the centre of the earth changes in direction, but its magnitude remains constant

the total mechanical energy of $S$ varies periodically with time

the linear momentum of $S$ remains constant in magnitude

Solution

Force on satellite is always directed towards earth, So, acceleration of satellite $S$ is always directed towards centre of earth. Net torque of this gravitational force $F$ about centre of earth is zero. Therefore , angular momentum (both in magnitude and direction) of $S$ about centre of earth is constant throughout. Since, the force $F$ is conservative in nature, therefore, mechanical energy of satellite remains constant. Speed of $S$ is maximum when it is nearest to earth and minimum when it is farthest.

Standard 11

Physics

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?

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Masses and radii of earth and moon are $M_1,\, M_2$ and $R_1,\, R_2$ respectively. The distance between their centre is $'d'$ . The minimum velocity given to mass $'M'$ from the mid point of line joining their centre so that it will escape

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$Assertion$ : 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.

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If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero

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The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be

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A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

Solution

Similar Questions

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?

Masses and radii of earth and moon are $M_1,\, M_2$ and $R_1,\, R_2$ respectively. The distance between their centre is $'d'$ . The minimum velocity given to mass $'M'$ from the mid point of line joining their centre so that it will escape

$Assertion$ : 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.

If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero

The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be

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$Assertion$ : 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.