Question

a 28. a satellite orbits the earth with a speed of 5.2×10³ m/s. what is the satellites distance from the centre of the earth?
a. 2.8×10⁶ m
b. 1.5×10⁷ m
c. 3.0×10⁷ m
d. 7.2×10⁷ m

Explanation:

Step1: Recall the formula for centripetal force and gravitational force

For a satellite in circular orbit, the centripetal force \(F_c = \frac{mv^{2}}{r}\) and the gravitational force \(F_g=\frac{GMm}{r^{2}}\). At equilibrium \(F_c = F_g\), so \(\frac{mv^{2}}{r}=\frac{GMm}{r^{2}}\), which simplifies to \(r=\frac{GM}{v^{2}}\). The mass of the Earth \(M = 6\times10^{24}\space kg\), the gravitational constant \(G=6.67\times 10^{- 11}\space Nm^{2}/kg^{2}\), and the speed of the satellite \(v = 5.2\times10^{3}\space m/s\).

Step2: Substitute the values into the formula

Substitute \(G = 6.67\times 10^{-11}\), \(M = 6\times10^{24}\), and \(v = 5.2\times10^{3}\) into \(r=\frac{GM}{v^{2}}\).

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Answer:

B. \(1.5\times10^{7}\space m\)