Answer:
7613 m/s
Explanation:
According to Newton's second law of motion, the net force (∑F) on the satellite is equal to its mass (m) times its acceleration (a). The only force on the satellite is the force due to gravity, which according to the Universal Law of Gravitation, is equal to the gravitational constant (G) times the mass of the planet (M) times the mass of the satellite (m) divided by the square of the distance (r) between their centers. Since the satellite is moving in a circle, it undergoes centripetal acceleration, which is equal to the square of the speed (v) divided by the radius (r).
[tex]\Large \text {$ \Sigma F=ma $}\\\\\huge \text {$ \frac{GMm}{r^2}=\ $}\Large \text {$ m $}\huge \text {$ \frac{v^2}{r} $}\\\\\Large \text {$ GM=v^2r $}\\\\\Large \text {$ v^2=\ $}\huge \text {$ \frac{GM}{r} $}\\\\\Large \text {$ v=\ $}\huge \text {$ \sqrt{\frac{GM}{r}} $}\\\Large \text {$ v=\ $}\huge \text {$ \sqrt{\frac{(6.67\times 10^{-11})(5.97\times 10^{24})}{6,370,000\ +\ 500,000}} $}\\\\\Large \text {$ v=7613\ m/s $}[/tex]
