Can you help me answer these questions?

Problem #1: After the Apollo missions 18, 19, and 20 were scrubbed due to budgetary cuts, long term space habitation became the central focus of NASA. Unused Saturn V's became the shell of the first space station, known as Sky Lab. An international collaboration was then created to fund living in space, which is still in existence - the international Space Station. One biological issue is the freefall orbit of these stations, which means that astronauts must work to maintain bone and muscle integrity. An idea to counter this is to \"create artificial gravity\" through the rotation of a space station. Suppose a space station was built in the form of a giant wheel with some diameter d. a. Derive an expression that gives the required period of rotation to produce artificial gravity equivalent to Earth's g. b. It has been thought that revolution rates greater than 2.0 revolutions per minute would cause astronauts to become dizzy what is the minimum diameter for the space station to avoid this? Problem #2: The first mission to the Earth's moon was accomplished during the Apollo 8 mission, which was launched on December 215t, 1968. Iconic photographs came from the mission, including the \"Earth rise," which highlighted what the Earth looked like from moon. This was also only the third launch of the Saturn V rocket, which is still the most powerful rocket used in manned space missions. Astronauts were placed into uniform circular orbit 112,000 meters above the moon's surface with an orbital period of 120.5 minutes. The radius of the moon was known to be 1,740,000 meters. a. From this information, find the mass of the moon. b. Determine the orbital velocity of the Apollo 8 command module, and also find its angular velocity. c. Apollo 8 spent about 20 hours in orbit with the moon. How many revolutions did it make around the moon? What angular displacement would this correspond to? How much linear distance was covered? d. Ifthe command module had been twice as massive, how would this have changed the orbital velocity of the Apollo 8 spacecraft? Explain your