At what speed should a satellite fly in order to move in a circle while "falling" to the Earth with acceleration g? Assume the orbit radius R = 6400 km and g = 10 \frac{m}{s^2}.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.3">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.3.21.$ At what speed should a satellite fly in order to move in a circle while "falling" to the Earth with acceleration $g$? Assume the orbit radius $R = 6400$ km and $g = 10$ $\frac{m}{s^2}$.
    </p>

    <h3>Solution</h3>
    <p>
        <p>

Equilibrium condition: centrifugal force compensates for gravitational force

$$mg = \frac{mv^2}{R}$$

Where, the desired speed

$$v = \sqrt{gR}=8\text{ km/s}$$

    <h4>Answer</h4>
    <p>
        $$v = \sqrt{gR}=8\text{ km/s}$$
    </p>


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