At liftoff maximum thrust is 7.69 E6 Newtons.The space vehicle consists of the Falcon 9 booster rocket for the first stage, a single engine booster for the second stage and the spacecraft/satellite. The payload typically consists of about 50 Starlink satellites for communication which are put into low earth orbit. There are now about3600 Starlink satellites in the Space Constellation.Most propellant is consumed in the first three minutes; orbital processing does not start until 28 minutes. Table 1 provides key information needed to perform the calculations to answer the questions that follow The launch vehicle consists of the first stage, called the Falcon 9, the second stage, and the spacecraft to be placed into orbit.YOUR ASSIGNMENTa. Calculate the rate of fuel consumption (RFC) at liftoff when maximum thrust occurs (kg/sec). See Row 1b. Calculate the rate of acceleration at lift off.c. Assume for a test that system hovers at lift off so that there is no acceleration. Calculate necessary thrust.d. Given the average thrust at row 2 calculate fuel consumption rate (RFC1) in kg/sec until MECO (see row 11)e. What is the acceleration immediately before MECO?f. Calculate total fuel burned until MECO based on average thrustg. Calculate mass of spacecraft (M1) in KG, before main engine separationh. Calculate vehicle velocity (Vbo) at time MECO. See page 626 of text, equation f. This equation will also be used for reentry and soft landing. Use the value for M1 as Mf in the equation and initial mass of spacecraft as MO.i. Calculate the height of vehicle at MECO (Hbo, egn e)j. The booster continues upward vertical velocity but decelerates linearly with time due to gravity. Calculate maximum altitude that booster reaches. (When velocity is zero)k. Calculate the propellant mass remaining in the main engine, PM1.I. Calculate current mass of the Main Engine, M2.m. Until reentry burn, assume 10,000 kg of cold gas is used, in the cold gas thrusters. Now the mass is M3.n. The same thrust equation is used to lower velocity as to increase velocity. Entry burn starts at altitude of approximately 63 km. Velocity is to be reduced from 1000 m/sec to 580 m/sec in 25 seconds. What is the new Engine Mass M4?o. Assume 5,000 kg of cold gas is used until landing burn by the thrusters for attitude control, now the mass is M5.p. For Landing burn, the vertical velocity is reduced from 170 m/sec to 0 m/sec in 23 seconds. What is M6, the Main engine mass after landing?q. Compare M6 to Mass of Main engine at Row 5

Table 1. Heavy Falcon Specications 1 Maximum thrust at launch 7,69E06 newtons 2 Average Thrust from launch until 6.25E06 Main Engine Cutout (MECO) newtons 3 Total Vehicle mass at liftoff 549,054 kg This value is MO 4 Payload for leo orbit 22,254 kg 5 Mass of Main Engine (Falcon 9 first 421,300 kg stage booster) full of PROPELLANT and Cold Gas 6 Main Engine , Empty of propellant 25,600 kg 7 Mass of propellant in Falcon 9, PMO 395,700 kg 8 Mass of Second stage full of 105,500 kg propellant 9 Timeline (based on videos) 10 Lift off T+0 11 First stage (Main engine) Cut off 2 min:30 sec (MECO) 12 Main engine separates from space 2:40 vehicle Table 2 Continued 13 Main engine maximum altitude See question Zero vertical velocity 14 Boost back, ip maneuvers, attitude 5:43 control 15 Begin Entry burn 6:20 16 End entry burn 6:45 17 Begin Landing burn 8:04 18 Soft Land and end landing burn 8:27 19 Go (gravity acceleration at all 9.8 m/sls altitudes) 20 ISP 280 seconds MAE 381 - Equations on page 664 of the textbook for HW 7 burnout time tho is m- m IboMAE 381 - Equations on page 664 of the textbook for HW 7 burnout time tho is m - m 1, = T The burnout altitude 12 hbo mitm - me m - me = m In- So me me The velocity at burnout Vbo = cln- mo - 80 (m - my) me