A satellite m = 500 kg orbits the earth at a distance d = 240 km, above the surface of the planet. The radius of the earth is re = 6.38 × 106 m and the gravitational constant G = 6.67 × 10-11 N m2/kg2 and the Earth's mass is me = 5.98 × 1024 kg.

During your summer internship for an aerospace company, you are asked to design a small research rocket. the rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 910 m above the earth's surface. the rocket's engines give the rocket an upward acceleration so it moves with acceleration of 16.0 m/s2 during the time t that they fire. after the engines shut off, the rocket is in free fall. ignore air resistance.

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

What is the weight of a feather (mass = 0.0001 kg) that floats through earth's and the moon's atmospheres?