Two particles of equal mass '$m$' move in a circle of radius '$r$' under the action of their mutual gravitational attraction. The speed of each particle will be:

What is the period of revolution of an Earth satellite? Ignore the height of the satellite above the surface of the Earth.
Given:
$(1)$ The value of gravitational acceleration $g = 10 \ ms^{-2}$.
$(2)$ Radius of Earth $R_E = 6400 \ km$. Take $\pi = 3.14$.

What are the conditions necessary for a satellite to appear stationary? What is the direction of rotation of a geostationary satellite?

Given below are two statements:
Statement $I$: $A$ satellite is moving around the Earth in an orbit very close to the Earth's surface. The time period of revolution of the satellite depends upon the density of the Earth.
Statement $II$: The time period of revolution of the satellite is $T = 2\pi\sqrt{\frac{R_e}{g}}$ (for a satellite very close to the Earth's surface), where $R_e$ is the radius of the Earth and $g$ is the acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below:

The time period of an artificial satellite in a circular orbit of radius $R$ is $2$ days and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16$ days,then :-

Does the orbital velocity of a planet depend on its mass?