Question

The Mars Reconnaissance Orbiter (launched on 8/12/2005) achieved a nearly circular orbit in September 2006 with a period of T = 6.72 x 10³ s. The mass, M, of Mars is 6.417 x 10²³ kg and its radius, R_Mars, is 3.39 x 10⁶ m.

The mass, m, of the Orbiter is 1,031 kg.

1) The Net Radial Force, ΣF_r, acting on the Orbiter as it orbits Mars, is due to the gravitational force between it and Mars. ΣF_r = GMm/r², where r is the orbital radius.

True or False

2) This Net Radial Force, ΣF_r, is also equal to mv²/r = m(2π/T)²r.

True or False

3) Accordingly, r = [GM(T/2π)²]^1/3

True or False

4) The speed, v, and the radius, r, of the Orbiter depend on the Orbiter's mass.

True or False

5) The Orbiter is _____x 10⁶ m from the center of Mars. Show your answer with the correct number of significant figures.

True or False

6) How many times does the Orbiter circle Mars in one earth day? (Show three significant figures in your answer. Don't try to use exponential notation. Use numbers like 3.76 or 15.9)

7) The value of g, gravitational acceleration, near the surface of Mars is ______ m/s².

8) An engineer is planning to put another satellite around Mars with a radius of r = 4.000 x 10⁷ m. Its speed in m/s would be:

9) What is the period, T, of the above planned satellite in earth days (to 2 significant figures)?

Answer 1