You are Sergei Korolev, chief Soviet rocket scientist, and have developed the bright idea of putting a big hunk of metal and electronics into orbit around Earth. You call it Sputnik 1 (you have apparently already assumed you will have to do this more than once) and wish to place it into a circular orbit 223 km above the earth's surfaceWhat speed (linear velocity), period, and radial (centripetal) acceleration must it have? The earth's radius is 6.38 * 10 ^ 6 m and its mass is 5.98*10^ 24 kg

Problem 3. A tracking station determines that an Earth-observation satellite has perigee and apogee altitudes of 350 and 1,206 km, respectively. Determine the orbital period (in minutes) and the parameter p.

Hello I needed help with this question.

The spaceship Palomino approaches star XYZ to study it by going into a circular orbit of radius 1.0·107 km. All that is known initially is that a planet orbits this star at a distance of 1.86·108 km taking a time of 271 Earth-days to make one full orbit. At what speed should the ship orbit the star at? What is the gravitational acceleration on the Palomino due to this star's gravity? (c) What is the ratio of the mass of star XYZ with that of the Sun? (MSun = 1.987·1030 kg)

4. We are planning a human exploration mission to Mars. We will first place our spacecraft into a circular around Mars and then send down a lander. a) If we want the spacecraft to orbit at an altitude of 170 km above the Martian surface, what will the velocity and orbital period of the spacecraft? b) When we land astronauts on the surface of Mars, what acceleration due to gravity in terms of g's (i.e. as a fraction of the Earth's gravitational acceleration) will the astronauts experience? You are permitted to use an online resource (e.g. Google) to find the necessary information about Mars that you might need in solving this problem.