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

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

1) The Net Radial Force, ΣF_r, acting on the Orbiteras it orbits Mars, is due to the gravitational force between it andMars. ΣF_r = GMm/r², where r is the orbitalradius.

True or False

2) This Net Radial Force, ΣF_r, is also equal tomv²/r = m(2Ï€/T)²r.

True or False

3) Accordingly, r =[GM(T/2Ï€)²]^1/3

True or False

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

True or False

5) The Orbiter is _____x 10⁶ m from the center ofMars. Show your answer with the correct number of significantfigures.

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 useexponential notation. Use numbers like 3.76 or 15.9)

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

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

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