When a satellite going round the earth in a circular orbit of radius r and speed v loses some of

step 1 Here I've drawn the Earth with a satellite represented by a box, orbiting the Earth at a radius

When a satellite going round the earth in a circular orbit...

When a satellite going round the earth in a circular orbit of radius $\mathrm{r}$ and speed $\mathrm{v}$ loses some of its energy, then $\mathrm{r}$ and $\mathrm{v}$ changes as (A) $r$ and $v$ both will increase (B) $\mathrm{r}$ and $\mathrm{v}$ both will decease (C) $r$ will decrease and $\mathrm{v}$ will increase (D) $\mathrm{r}$ will increase and $\mathrm{v}$ will decrease

When a satellite going round the earth in a circular orbit of radius $\mathrm{r}$ and speed $\mathrm{v}$ loses some of its energy, then $\mathrm{r}$ and $\mathrm{v}$ changes as
(A) $r$ and $v$ both will increase
(B) $\mathrm{r}$ and $\mathrm{v}$ both will decease
(C) $r$ will decrease and $\mathrm{v}$ will increase
(D) $\mathrm{r}$ will increase and $\mathrm{v}$ will decrease

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Key Concepts

Circular Orbit Mechanics

This concept involves understanding that in a circular orbit, the gravitational force provides the necessary centripetal force that keeps the satellite moving along its circular path. The relationship is defined by the balance between gravitational force and the centripetal force requirement, leading to the orbital speed being determined by the equation v = ?(GM/r), where G is the gravitational constant, M is the mass of the central body, and r is the orbital radius.

Orbital Energy and Its Impact on Orbital Parameters

This concept focuses on how the total mechanical energy of a satellite in orbit, which is a combination of its kinetic and potential energy, influences its orbit. A loss of energy, such as through friction or other non-conservative forces, results in a decrease in orbital radius. Due to the inverse relationship between orbital speed and radius in circular orbits, a decrease in radius leads to an increase in speed. Understanding this energy relationship is key to predicting how changes in the satellite's energy state affect its orbital parameters.

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