Problem

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)

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/8085/

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