Two planetoids with radii R1 and R2 and local accelerations g1 and g2 are separated by a centre-to-centre distance D, and are members of a simple two-body system. A rocket is located on planetoid 1 and is scheduled to launch from this planetoid to a point between the planetoids where the net gravitational force on the rocket by the two planetoids is zero. At what distance from the centre of planetoid 1 is the zero gravitational point? Choose R1 = 1400m, R2 = 1000m, g1 = 7.5m/s2, g2 = 5.3m/s2 and D = 4800m. [5 points]

1. consider the case in which air fills air shocks on a truck trailer. the pressure in the shocks is 2 mpa. the temperature is 300 k. the diameter of the shock piston is 10 cm and the initial length of the cylindrical cavity containing the compressed air is 40 cm. a. the truck is gradually loaded over a period of a day in a static setting. the temperature is held constant for the atmosphere and thus for the gas shock. calculate the compressibility of the air in the shock for this condition when the truck is initially being loaded. b. if the shocks were loaded in a dynamic setting by driving over bumps, what would be the compressibility? state your assumption. c. what is the initial load on the shock if the shock is in an atmospheric 100 kpa? d. if the shock is compressed using the process described in part a, and the air shock compressed air cavity length decreases to 20 cm, what is the additional load applied to the shock?