Describe your approach to calculating the velocity of a satellite in an orbit of radius R around the Earth Select as many options as you think are appropriate. Use Newton's second law Use Kepler's second law Use Newton's law of universal gravitation Use Kepler's first law

Review. In 1963, astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit, he aged two-millionths of a second less than he would have had he remained on the Earth. (a) Assuming Cooper was 160 km above the Earth in a circular orbit, determine the difference in elapsed time between someone on the Earth and the orbiting astronaut for the 22 orbits. You may use the approximation 11x=1+x2 for small x. (b) Did the press report accurate information? Explain.

It has been suggested that rotating cylinders about 20 km in length and 8 km in diameter be placed in space and used as colonies. The purpose of the rotation is to simulate gravity for the inhabitants. Explain this concept for producing an effective imitation of gravity.

The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the sufrace.) (a) Calculate the acceleration due to the Moon’s gravity at that point. (b) Calculate the centripetal accelereation of he center of Earth a sit rotates about that point once each lunar month (bout 27.3 d) and compare it with the acceleration found in part (a). Comment on whether or not they are equal and why they should or should not be.

Unreasonable Result A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight. (a) Calculate the mass of the mountain. (b) Compare the mountain's mass with that of Earth. (c) What is unreasonable about these results? (d) Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)

Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.

According to the National Academy of Sciences, the Earths surface temperature has risen about 1F since 1900. There is evidence that this climate change may be due to human activity. The organizers of World Jump Day argue that if the Earth were in a slightly larger orbit, we could avoid global warming and climate change. They propose that we move the Earth into this new orbit by jumping. The idea is to get people in a particular time zone to jump together. The hope is to have 600 million people jump in a 24-hour period. Lets see if it will work. Consider the Earth and its inhabitants to make up the system. a. Estimate the number of people in your time zone. Assume they all decide to jump at the same time; estimate the total mass of the jumpers. b. What is the net external force on the Earthjumpers system? c. Assume the jumpers use high-tech Flybar pogo sticks (Fig. P8.32), which allow them to jump 6 ft. What is the displacement of the Earth as a result of their jump? d. What happens to the Earth when the jumpers land?

Respond to each statement, true or false: (a) No force of gravity acts on an astronaut in an orbiting space station. (b) At three Earth radii from the center of Earth, the acceleration of gravity is one-ninth its surface value. (c) If two identical planets, each with surface gravity g and volume V, coalesce into one planet with volume 2V, the surface gravity of the new planet is 2g. (d) One kilogram of gold would have greater value on Earth than on the Moon.