Question

multiple choice question
which equation is most helpful in determining the speed of a satellite in a circular orbit around earth?

○ $ma = \frac{mv^2}{r}$

○ $\frac{gm_em}{r^2} = \frac{mv^2}{r}$

○ $\frac{gm_em}{r} = \frac{1}{2}mv^2$

○ $\frac{gm_em}{r^2} = ma$

Explanation:

Step1: Identify centripetal force source

The gravitational force between Earth and satellite provides centripetal force for circular orbit. Gravitational force is $\frac{GmEms}{r^2}$ (corrected typo: $r^2$ denominator), centripetal force is $\frac{mv^2}{r}$.

Step2: Equate the two forces

Set gravitational force equal to centripetal force: $\frac{GmEms}{r^2} = \frac{mv^2}{r}$. This equation can solve for speed $v$.

Answer:

B. $\frac{GmEms}{r^2} = \frac{mv^2}{r}$ (Note: Assuming the second option has a typo in $r2$ which should be $r^2$)