Final answer:
The question's answer requires the use of Kepler's third law to calculate the orbital period of the Mars Reconnaissance Orbiter. However, without the mass and radius values for Mars, this calculation cannot be completed here. The Mars Climate Orbiter's crash due to a unit conversion error highlights the importance of accurate measurements in orbital calculations.
Step-by-step explanation:
To calculate how long it takes for the Mars Reconnaissance Orbiter to orbit Mars at an altitude of about 275 km, we can use Kepler's third law, which relates the orbital period of a satellite to the radius of its orbit around the central body (in this case, Mars). Given the mass and radius of Mars, which are essential inputs for applying Kepler's law, we could calculate the precise orbital period. However, the question does not provide these values, so we cannot compute the period here.
As a related example, when applying Kepler's third law to the Mars Climate Orbiter, there was an error that resulted from confusing English units with SI units, which caused the spacecraft to enter the Martian atmosphere at a dangerously low altitude of 57 km, leading to its destruction.
By converting 187,000 feet to kilometers using the conversion that 1 meter equals 3.281 feet, 187,000 feet is approximately 57 km, which provides insight into how close the Mars Climate Orbiter was to the surface of Mars before its demise.