A satellite moves in a stable circular orbit round the earth if (where $\mathrm{V}_{\mathrm{H}},…

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)
  1. $\mathrm{V}_{\mathrm{H}} < \mathrm{V}_{\mathrm{c}}$
  2. $\mathrm{V}_{\mathrm{H}}=\mathrm{V}_{\mathrm{e}}$
  3. $V_H=V_c$
  4. $\mathrm{V}_{\mathrm{H}}>\mathrm{V}_{\mathrm{e}}$

Solution

Since the satellite is in a stable circular orbit, its horizontal velocity VH must be equal to the critical velocity Vc to maintain equilibrium between the gravitational force and the centripetal force. Therefore, option (c) $V_H=V_c$ is correct. .

Asked in: MHT CET 2023 (10 May Shift 1)

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