Suppose NASA wants a satellite to revolve around Earth 5 times a day.What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg) A)1.44 × 10⁷ m B)0.69 × 10⁷ m C)7.22 × 10⁷ m D)2.11 × 10⁷ m

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Quizplus · Accepted Answer

The orbital period $T$ can be calculated using the formula for the orbital period of a satellite revolving around Earth, $T = 2\pi\sqrt{\frac{r^3}{GM}}$, where $r$ is the radius of the orbit, $G$ is the gravitational constant, and $M$ is the mass of Earth. Given that the satellite revolves around Earth 5 times a day, we can convert this to seconds to find $T$. Since there are 86400 seconds in a day, $T = \frac{86400}{5}$ seconds for each orbit. Rearranging the formula to solve for $r$ and substituting the given values for $G$ and $M_{earth}$, we find that the radius $r$ that satisfies the condition for 5 orbits per day is closest to the value given in option A, $1.44 \times 10^7 m$. This calculation involves algebraic manipulation and substitution into the rearranged orbital period formula.

Suppose NASA Wants a Satellite to Revolve Around Earth 5