Final answer:
To find the orbital speed of the Westar VI satellite 600 km above the Earth's surface, use the formula v = √(GM/r), accounting for the altitude in the value of r and considering the Earth's mass and gravitational constant.
Step-by-step explanation:
To determine the speed of a satellite orbiting the Earth, such as the Westar VI satellite in a circular orbit 600 km above the Earth's surface, we can use the formula for circular orbital speed derived from setting the gravitational force equal to the required centripetal force for circular motion. The formula is v = √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite.
Substituting the given values into the formula (with G and M known constants, and r equal to the radius of the Earth plus the altitude of the satellite), and knowing the gravitational acceleration (g) at the satellite's altitude (8.22 m/s²), we can solve for the satellite's orbital speed. The free-fall acceleration provides additional information about the strength of gravity at the altitude of the satellite, which could also be used with the formula v = √(g · r) when g is known at that particular altitude and r includes the altitude above the Earth's surface.