Can a satellite be in an orbit in a plane not passing through the earth’s cantre?

Can a satellite be in an orbit in a plane not passing through the earth’s cantre? Explain .

Ans.     The centripetal force required for the orbital motion of the satellite is provided by the gravitational force of attraction. Gravitational force is a central force, i.e.., it passes through the centre of mass of the earth and the satellite. Hence, the plane of orbit of the satellite has to pass through the earth’s centre.

Why a spacecraft consume more fuel in going from earth to moon than it does on the return trip ?

A spacecraft consume more fuel in going from earth to moon than it does on the return trip. Comment on this.

Ans.     In going from earth to moon, the spacecraft has to do more work against the greater gravitational attraction of the earth. For the return journey, moon’s gravitational force is much less, hence less work is done and less fuel is consumed.

Why are space crafts usually launched from west to east?

Why are space crafts usually launched from west to east? Why is it more advantageous to launch rockets in the equatorial plane?

Ans.     Earth rotates on its axis from west to east. A satellite launched from west to east will have the advantage of the additional velocity of the earth’s rotation. The effect is maximum  at the equator, hence it is most advantageous to launch the satellite from west to east on the equatorial plane.

Inertial & Gravitational Masses

INERTIAL AND GRAVITATIONAL MASSES:
(i) Inertial masses :– It is a measure of the ability of a body to oppose the production of acceleration in it by an external force. It also measure inertia of a body.
Let F be applied force on a body which produces an acceleration a
Then, F = ma
m = F/a
(i) Gravity has no effect on the inertial mass of the body
(ii) Inertial mass does not depends upon the size, shape and state of the body
(iii) Inertial mass of a body does not depend upon on the presence or absence of other bodies near it.
(iv) Inertial mass of a body is directly proportional to the quantity of matter contained in the body.
(v) Inertial mass of the body increases with increase in velocity.
m= mo/(1-v2/c2)1/2
Where mo is mass of a body at rest
v is velocity of the body
c is the velocity of the light in vacuum.
Gravitation of Mass :–
It is defined as mass of body which determines the magnitude of gravitational pull between the body and the earth. Let F be the gravitational force on a body of mass m due to earth
Then F = GMm/R2
Where R is the radius of earth
M is the mass of earth
m = FR2/GM
The mass of body determined in this way is the gravitational mass of the body.
Gravitational mass is same as inertial mass in all respect, except in the method of their measurement.

What is the Reasons For Weightlessness ?

Reasons For Weightlessness :
Sol: 1. Any artificial satellite itself in a state of weightlessness condition becomes total earth gravitational force is balanced by centripetal force in order to orbiting the satellite in the given stable orbital.
2. Weightlessness conditions for any body placed inside the satellite can be employed in the following ways :
(a) Centrifugal force experienced by inside the body is neutralized by earth gravitational force.
(b) There is no normal reaction experienced by body from the surface to satellite because it is treated as point mass.
(c) Any body having zero relative acceleration with respect to satellite.