Question

Spacecraft have been sent to mars in recent years. mars is smaller than earth and has correspondingly weaker surface gravity. on mars, the free-fall acceleration is only 3.8 m/s2 . you may want to review (pages 174 - 175) . part a what is the orbital period of a spacecraft in a low orbit near the surface of mars? assume the radius of the satellite's orbit is about the same as the radius of mars itself, rmars = 3.37×106 m .

a) 1.78 hours
b) 2.14 hours
c) 2.88 hours
d) 3.26 hours

Answer 1

To calculate the orbital period of a spacecraft in a low orbit near the surface of Mars, we can use Kepler's third law. The orbital period can be calculated using the formula: T = 2π√(r^3/GM). Plugging in the values, we find that the orbital period is approximately 2.14 hours.

Step-by-step explanation:

To calculate the orbital period of a spacecraft in a low orbit near the surface of Mars, we can use Kepler's third law. According to Kepler's third law, the square of the orbital period is proportional to the cube of the radius of the orbit. In this case, the radius of the satellite's orbit is about the same as the radius of Mars itself, which is 3.37×10^6 m. The orbital period of the spacecraft can be calculated using the formula: T = 2π√(r^3/GM), where T is the orbital period, r is the radius of the orbit, G is the gravitational constant (6.67×10^-11 N m^2/kg^2), and M is the mass of Mars (6.418×10^23 kg).

Plugging in the values, we get:

T = 2π√((3.37×10^6)^3/(6.67×10^-11 × 6.418×10^23))

Simplifying the expression and calculating the value, we find that the orbital period is approximately 2.14 hours. Therefore, the correct answer is (b) 2.14 hours.