A satellite is placed in equatorial orbit above Mars, which has a radius of 3397 km and a mass M_M = 6.40 × 10²³ kg. The mission of the satellite is to observe the Martian climate from an altitude of 488 km. What is the orbital period of the satellite? A)9.18 × 10² s B)3.62 × 10³ s C)7.36 × 10³ s D)1.08 × 10⁵ s E)7.27 × 10¹² s

Question

Quizplus · Accepted Answer

The orbital period of a satellite in circular orbit can be calculated using the formula:
T = 2π√(r^3/GM), where r is the radius of the orbit, G is the gravitational constant, and M is the mass of the planet being orbited.
In this case, the radius of the orbit is the sum of the radius of Mars and the altitude of the satellite above Mars:
r = 3397 km + 488 km = 3885 km = 3.885 × 10^6 m
Plugging the values into the formula, we get:
T = 2π√((3.885 × 10^6)^3/(6.67 × 10^-11 × 6.40 × 10^23)) = 7.36 × 10^3 s = 7.36 × 10^13 ms
Therefore, the best choice is C, 7.36 × 10^13 ms or 7.36 × 10^3 s.

A Satellite Is Placed in Equatorial Orbit Above Mars, Which