7.) With what velocity must a satellite be injected into orbit around Earth, if its orbit is to have a radius of $6.90 \times 10^{6} \mathrm{~m} ?$ (4 marks)
Answer
\(\boxed{7600.26}\) m/s is the required velocity for the satellite to be injected into orbit.
Step 1 ：Given the radius of the orbit, r = \(6.90 \times 10^{6}\) m, the gravitational constant, G = \(6.674 \times 10^{-11}\) N(m/kg)^2, and the mass of Earth, M = \(5.972 \times 10^{24}\) kg.
Step 2 ：Use the formula for the velocity of a satellite in orbit: v = \(\sqrt{\frac{G \times M}{r}}\)
Step 3 ：Substitute the given values into the formula: v = \(\sqrt{\frac{(6.674 \times 10^{-11})(5.972 \times 10^{24})}{6.90 \times 10^{6}}}\)
Step 4 ：Calculate the velocity: v ≈ 7600.26 m/s
Step 5 ：\(\boxed{7600.26}\) m/s is the required velocity for the satellite to be injected into orbit.
