4 Reusable First Stage y1 = 15.338 m m1 = 2.047 x 10 kg 5 y2 = 5.115 m m2 = 1.613 x 10 kg By Tamman Montanaro

What is the moment of inertia? What is the force required from the cold gas thrusters if we assume constancy. Figure 1. Robbert Goddard’s design of the first ever to fly in 1926. Source: George Edward Pendray. The moment of inertia of a solid disk: rper The Rocket Formula

Now lets stack a bunch of these solid disk on each other:

Length = l Divide by dt Figure 2: Flight path for the ; After separation, the first stage orientates itself and prepares itself for . Source: SpaceX

If we do the same for the hollow cylinder, we get a moment of inertia Launch of: for a rocket: How much mass is lost? What is the mass loss?

What is the moment of inertia about the center of mass for these two objects? Divide by m Figure 3: Falcon 9 first stage after landing on drone barge. Source: SpaceX

nd On December 22 2015, the Falcon 9 -2 What is the constant force required for its journey halfway (assuming first stage lands successfully. This is the first ever orbital- that the force required to flip it 90o is the equal and opposite to class rocket landing. From the video and flight logs, we Flip Maneuver stabilize the flip). can gather specifications about the first stage. ⃑ How much time does it take for the first stage to descend? We assume this is the time it takes � Flight Specifications for the first stage to reorientate itself.

Thrust @vac = 7.543 MN Hfirst stage = 40.9 m Assuming constant alpha: Total Mass = 5.135 x 105 kg Burn Time = 102 seconds �⃑ First Stage Mass = 3.975 x V = 1666 m/s cutoff 0 5 With t = 62 sec, � = 90 , and r = 29.53 m 10 kg Hcutoff = 75.5 km Propellant Mass = 3.728 x = 620 km x 660 km x What is the center of mass? Let us think of the first stage in two parts: a uniform hollow and 105 kg 47o solid cylinder stacked on one another. Assume cold gas thrusters that provide the force to flip Isp @vac = 312 seconds Merlin 1D mass(first stage) = are at a height of 35.8 meters and that the height of separation is 10.23 meters. 4230 kg

Source: SpaceX (web, launch video, flight logs)