I only need help with part b. please be descriptive and do the math and draw the GS please.

1) (10 Points) On its mission to explore the UNIVERSE, the USS Enterprise ( ME= 100,000 [ kg ] ) discovers an infinite length rod in an otherwise empty region of space. The captain decides to send out a probe to study the properties of the rod. The Enterprise "parks" 200 [km] from the rod, holding itself at rest relative to the rod by applying a constant thrust force away from the rod with a magnitude of 1 [MN] (1 [MN] = 1,000,000 Newtons). It then fires out a "probe" which is effectively a bowling ball with a mass m,=20[kg ] and charge 9:=+5[uC] . The "probe" moves about the rod in a circular orbit with speed 15,000 [m/s]. a) Draw a FBD of the (uncharged) Enterprise at rest near the rod. b) Use Gauss' Law for Gravity to find an expression for the gravitational field due to the infinite length rod a distance r away in terms of the linear mass density of the rod ,, . GL for gravity is & g. dA=-4nGm where mene is the mass enclosed by your chosen Gaussian surface (GS). HINT: You must draw your GS and go through the steps. c) Find the linear mass density Am, of the rod. d) Draw a FBD of the orbiting bowling ball "probe" e) Find the linear charge density