Question

let ( g ) be the universal gravitational constant and ( m_p ) be the mass of the planet a satellite is orbiting. which equation could be used to find the velocity of the satellite if it is placed in a low earth orbit? (1 point)
options (formulas with some terms like ( \frac{1}{(3000 \text{km})}sqrt{gm_p} ), ( sqrt{\frac{gm_p}{(3000 \text{km})}} ), ( sqrt{\frac{gm_p}{(300 \text{km})}} ), ( \frac{1}{(300 \text{km})}sqrt{gm_p} ) shown with radio buttons)

Explanation:

Step1: Recall orbital velocity formula

The orbital velocity of a satellite in a circular orbit is derived by equating gravitational force to centripetal force, giving the base formula:
$$v = \sqrt{\frac{Gm_p}{r}}$$
where $r$ is the orbital radius (distance from the planet's center; for low Earth orbit, this is approximately the planet's radius, here represented as a value in km).

Step2: Match to given options

Comparing the derived formula to the choices, the correct structure is a square root of $\frac{Gm_p}{r}$, where $r$ is the low Earth orbit radius (the denominator inside the square root).

Answer:

$\boldsymbol{v = \sqrt{\frac{Gm_p}{(6380\ \text{km})}}}$ (the second option listed)