If r represents the radius of the orbit of a satellite of...

If $\mathrm{r}$ represents the radius of the orbit of a satellite of mass m moving around a planet of mass $\mathrm{M}$, the velocity of the satellite is given by (A) $\mathrm{U}^{2}=(\mathrm{gM} / \mathrm{r})$ (B) $\mathrm{U}^{2}=[(\mathrm{GMm}) / \mathrm{r}]$ (C) $\mathrm{U}=(\mathrm{GM} / \mathrm{r})$ (D) $\mathrm{U}^{2}=(\mathrm{GM} / \mathrm{r})$

If $\mathrm{r}$ represents the radius of the orbit of a satellite of mass m moving around a planet of mass $\mathrm{M}$, the velocity of the satellite is given by
(A) $\mathrm{U}^{2}=(\mathrm{gM} / \mathrm{r})$
(B) $\mathrm{U}^{2}=[(\mathrm{GMm}) / \mathrm{r}]$
(C) $\mathrm{U}=(\mathrm{GM} / \mathrm{r})$
(D) $\mathrm{U}^{2}=(\mathrm{GM} / \mathrm{r})$

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Key Concepts

Newton's Law of Universal Gravitation

This principle explains that every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It establishes the foundation for understanding gravitational interactions between celestial bodies.

Centripetal Force in Circular Motion

For an object to maintain a circular orbit, there must be a net inward force, called the centripetal force. In the context of orbital motion, the gravitational force provides this necessary centripetal force, ensuring that the satellite remains in a stable, circular orbit.

Orbital Velocity

Orbital velocity is the speed at which an object must travel to balance the gravitational pull acting as the centripetal force. By equating the gravitational force to the centripetal force, one can derive the formula for orbital velocity, which shows that the square of the velocity is proportional to the gravitational constant and the mass of the central body, and inversely proportional to the orbital radius.

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