Question

The length of time a satellite takes to orbit the earth depends on its:
(A) Launch speed.
(B) Mass.
(C) Distance from the earth.
(D) Weight.
(E) Orbital distance.

Answer 1

Hint: We know that the length of the time T taken by a satellite is given by - \[T = \dfrac{{2\pi }}{R}\sqrt {\dfrac{{{{\left( {R + h} \right)}^3}}}{g}} \].
It means T only depends upon the distance between satellite and earth.

Complete step by step answer:
We know that the length of the time T taken by a satellite is given by - \[T = \dfrac{{2\pi }}{R}\sqrt {\dfrac{{{{\left( {R + h} \right)}^3}}}{g}} \].
Here, R is the radius of the earth which is a constant. H is the distance of the satellite from the earth and g is the gyrational force which is again a constant.
It means the length of time T taken by a satellite-only varies when the distance between the satellite and earth is changed.
\[T \propto \sqrt {{{\left( h \right)}^3}} \]
It means when the distance between the satellite and the earth is changed then the length of the time taken T by a satellite will also change.
In option A we have launch speed, so the time taken by the length of the satellite is independent of launch speed.
In option B we have mass, we know that T is independent of mass so, option B is false.
In option C we have distance from the earth, we know that \[T \propto \sqrt {{{\left( h \right)}^3}} \] so, ‘T’ will change when the distance between earth and satellite is changed. So, option C is true.
In option D we weigh, we know that T is independent of mass so, option D is false similarly, in option E we have orbital direction, so we know that T is independent of orbital direction. option E is false.

Therefore, option C is correct.

Additional information:
A satellite is an object in space that revolves around a bigger object. There are two types of satellites, the first is the natural satellite and the second is an artificial satellite. Moon is a natural satellite whereas the satellite used in our communication, GPS is an artificial satellite.

Note:
One can confuse that the object having more mass will take more time so option B is correct, but it is Note:d that T is independent of mass i.e., if we change the mass of the satellite then even it will take the same time T to cover the same distance.