Satellites: Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.) A) 1.44 × 10⁷ m B) 0.690 × 10⁷ m C) 7.22 × 10⁷ m D) 2.11 × 10⁷ m

Question

Quizplus · Accepted Answer

To find the radius of the orbit, we can use the formula for the orbital period $T = 2\pi\sqrt{\frac{r^3}{GM}}$, where $T$ is the orbital period, $r$ is the radius of the orbit, $G$ is the gravitational constant, and $M$ is the mass of the Earth. Given that the satellite revolves around the Earth 5 times a day, we need to convert this into seconds to find $T$ (1 day = 86400 seconds, so $T = \frac{86400}{5}$ seconds). Rearranging the formula to solve for $r$ and substituting the given values for $G$ and $M$, we can calculate the radius $r$. The correct calculation leads to the radius in the order of magnitude of $10^{7}$ meters, which matches option A.

Satellites: Suppose We Want a Satellite to Revolve Around the Earth