An astronaut orbiting the earth is preparing to dock with a westar vi satellite. the satellite is in a circular orbit 700 km above the earth's surface, where the free-fall acceleration is 8.18 m/s2. take the radius of the earth as 6400 km. determine the speed of the satellite.

Find the volume of the ellipsoid x^2+y^2+5z^2=36.

How would you place two electrons on a sphere of radius r so that the electrostatic potential energy is minimized. how would you place three electrons to solve the same problem.

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.