Question 337: Gravitation

Question

A satellite moves in a stable circular orbit round the earth if (where $$\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}}$$ and $$\mathrm{V}_{\mathrm{e}}$$ are the horizontal velocity, critical velocity and escape velocity respectively)

Accepted Answer

To understand the conditions for a stable circular orbit around Earth, we need to know the meanings of the critical velocity ($\mathrm{V}_{\mathrm{c}}$) and escape velocity ($\mathrm{V}_{\mathrm{e}}$).
Critical Velocity ($\mathrm{V}_{\mathrm{c}}$) is the necessary orbital velocity a body must have to be in a stable circular orbit around Earth without the need for propulsion. It depends on the gravitational force providing the necessary centripetal force to keep the satellite in orbit.
Escape Velocity ($\mathrm{V}_{\mathrm{e}}$) is the minimum velocity an object must have to break free from the gravitational attraction of a celestial body, like earth, without further propulsion.
For a satellite to maintain a stable orbit, its horizontal velocity ($\mathrm{V}_{\mathrm{H}}$) must be equal to the critical velocity ($\mathrm{V}_{\mathrm{c}}$). If the horizontal velocity is less than critical velocity, the gravitational pull will cause the satellite to spiral downwards towards Earth. If the horizontal velocity is greater than critical velocity but less than escape velocity, the satellite will enter an elliptical orbit. And if the horizontal velocity equals or exceeds escape velocity, the satellite will leave Earth's orbit entirely.
In simple terms, for a stable, circular orbit, the option is:
Option C :
$$V_H=V_c$$
Options A and D would not result in a stable circular orbit. Option A would lead to a decaying orbit, and Option D would cause the satellite to leave orbit entirely. Option B implies that the satellite would be on an escape path and thus not in a stable orbit around the Earth.

Answer

$$\mathrm{V}_{\mathrm{H}}<\mathrm{V}_{\mathrm{c}}$$

Answer

$$\mathrm{V}_{\mathrm{H}}=\mathrm{V}_{\mathrm{e}}$$

Answer

$$V_H=V_c$$

Answer

$$V_H>V_e$$

Gravitation

A satellite moves in a stable circular orbit round the earth if (where $\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}} and \mathrm{V}_{\mathrm{e}}$ are the horizontal velocity, critical velocity and escape velocity respectively)

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