Problem 41
Be sure to show all calculations clearly and state your final answers in complete sentences. Imagine another solar system, with a star of the same mass as the Sun. Suppose there is a planet in that solar system with a mass twice that of Earth orbiting at a distance of 1 AU from the star. What is the orbital period of this planet? Explain. (Hint: The calculations for this problem are so simple that you will not need a calculator.)
Problem 42
Suppose a solar system has a star that is four times as massive as our Sun. If that solar system has a planet the same size as Earth orbiting at a distance of \(1 \mathrm{AU}\), what is the orbital period of the planet? Explain. (Hint: The calculations for this problem are so simple that you will not need a calculator.
Problem 43
The Moon orbits Earth in an average time of 27.3 days at an average distance of 384,000 kilometers. Use these facts to determine the mass of Earth. (Hint: You may neglect the mass of the Moon, since its mass is only about \(\frac{1}{80}\) of Earth's.)
Problem 44
Jupiter's moon Io orbits Jupiter every 42.5 hours at an average distance of 422,000 kilometers from the center of Jupiter. Calculate the mass of Jupiter. (Hint: Io's mass is very small compared to Jupiter's.)
Problem 45
Be sure to show all calculations clearly and state your final answers in complete sentences. Pluto's moon Charon orbits Pluto every 6.4 days with a semimajor axis of 19,700 kilometers. Calculate the combined mass of Pluto and Charon. Compare this combined mass to the mass of Earth, which is about \(6 \times 10^{24}\) kg. Can you determine the individual masses of Pluto and Charon from the given data? Explain.
Problem 48
Imagine that future humans decide to breed new organisms tailored to as many different environments as possible. Discuss some of the places in our solar system where we could potentially plant such artificially created species, even if life probably would not arise naturally in those places. Do you think it likely that we will someday develop life-forms for other worlds? What are the philosophical ramifications of being able to custom-tailor life for worlds that don't have any natural life?
Problem 49
Imagine that you are living a century from now and are taking a course about life in our solar system. Based on the current rate of exploration and reasonable rates for the future, how much more do you think we will know then about life in our solar system than we know now? Speculate about some of the discoveries you think may occur in the next century.
Problem 50
Learn more about NASA's Apollo project, the only set of missions that has ever sent humans to another world. Describe the goals and objectives of each of the Apollo missions. Which were successful, and which were not? What lessons does Apollo offer for future attempts to send humans to the Moon and beyond? Summarize your findings and your opinions about lessons for the future in a one- to two-page essay.
