A centripetal force of 235 N acts on a \( 1,050-\mathrm{kg} \) satellite moving with a speed of \( 5,300 \mathrm{~m} / \mathrm{s} \) in a circular orbit around a planet. What is the radius of its orbit? \( .24 \times 10^{\wedge} 8 \mathrm{~m} \)

Given: - Centripetal force, \( F = 235 \, \text{N} \) - Mass of the satellite, \( m = 1,050 \, \text{kg} \) - Speed of the satellite, \( v = 5,300 \, \text{m/s} \) - Radius of the orbit, \( r = ? \) The centripetal force acting on an object moving in a circular path is given by the formula: \[ F = \frac{mv^2}{r} \] We are given the centripetal force, mass, and speed of the satellite. We need to find the radius of its orbit. Rearranging the formula to solve for the radius, we get: \[ r = \frac{mv^2}{F} \] Substitute the given values into the formula to find the radius of the orbit. Calculate the value by following steps: - step0: Calculate: \(\frac{1050\times 5300^{2}}{235}\) - step1: Reduce the fraction: \(\frac{210\times 5300^{2}}{47}\) The radius of the orbit of the satellite is approximately \( 1.255085 \times 10^8 \, \text{m} \).