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Astronomy 4800 Homework #1 Answer Key

1. (4 pts). Should we explore ? Argue both sides of this question. Do some research on-line and develop arguments in a paragraph describing why we should explore space. Similarly, write another paragraph describing why space should not be a priority for the nation given the multiple draws on U.S. taxpayer dollars. Example response: Pro: Humankind has always been driven to explore, to learn, to expand boundaries. From Asian and Polynesian voyages eastward to European expeditions to the “New World” to Lewis and Clark venturing into the unknown American West, exploration is often driven by innate human curiosity. Space is no different. Space travel opens the to some of the most fundamental questions concerning our existence. How did we get here? Are we alone in the universe? The possibility of answering these questions is alone enough to warrant space travel and exploration. Con: The U.S. Federal Government currently owes over 28 trillion dollars in debt. Significant investment in space travel would require either increasing the national debt or cutting funding to another portion of the budget. The government cannot afford to spend millions of dollars on space missions that provide no tangible value. Federal taxpayer dollars would be better spent on issues directly affecting American quality of life such as social programs like medicare or public housing, rebuilding aging infrastructure, climate change, or developing renewable energy.

2. (6 pts). The Mission Directorate (SMD) at NASA is divided into four discipline areas: Science, , Heliophysics (study of the Sun and ), and Astrophysics. Go to NASA’s Science 2020-2024: A Vision for Scientific Excellence at: https://science.nasa.gov/science-pink/s3fs-public/atoms/files/2020- 2024_Science.pdf and read about the scientific goals and objectives, along with the current missions underway. a. Briefly describe the four priorities that NASA currently maintains for science. Elaborate on two that you think are most important and describe why. Example Response: NASA’s first priority is exploration and scientific discovery, which involves efforts to discover the secrets of the universe, search for life, and other important questions. The second priority is innovation, which is achieved through the development of new technologies and strategies to answer research questions. Third is interconnectivity and partnerships, which recognizes the importance of collaboration with a wide variety of people and organizations. Finally, inspiration involves encouraging and developing future leaders through engagement and public outreach. In my opinion, exploration and scientific discovery as well as inspiration are the two most important goals because they are closely aligned with public perception of NASA. Through the lunar landings and numerous scientific missions such as the Hubble , NASA has always been a beacon of both inspiration and scientific discovery. b. Then, compare and contrast today’s priorities with goals described in the paper Introduction to Outer Space (class website for Sep. 1) from 1958. How are things similar and how are they different from what was described to President Eisenhower? Example Response: The goals outlined in Introduction to Outer Space are exploration, development of technology, national prestige, and advancement of scientific knowledge. These goals are quite similar to NASA’s current stated priorities with the exception of national prestige. With the context of the and the , it makes sense that NASA would be much more focused on national prestige during Eisenhower’s presidency. Now, this has been replaced with a focus on (global) collaboration.

3. (4 pts). In class, we showed a graph of how government R&D funding as a share of GDP has declined over the past 60 years while industry funding has increased. a. Do a little research and discuss why you believe these funding trends developed as they did? Make sure to discuss the differences in funding and expected outcomes of R&D investments between government agencies and industry. Example Response: Ultimately, the responsibility for funding levels falls on those who construct and approve the budgets. For the federal government, this is the President and congress. For industry, it is the executives at a given company. Clearly those two groups as a whole have come to different conclusions regarding the relative importance of funding R&D. There are likely a myriad of reasons why government funding has consistently declined over the last few decade, including gridlock (e.g. shutdowns and difficulty passing budgets) or shifting political priorities to other subjects. R&D funding is not likely significant issue to most voters, so it may be easy for congress people to neglect it without damaging their electoral prospects. Additionally, government funding for R&D is often devoted to basic rather than applied research. While basic research still produces innovation and advances knowledge, it is often more abstract and does not always address a practical problem or application. Funding for basic research may be hard to justify to taxpayers without a direct application or end product to show for it. On the other hand, industry executives have clearly concluded that increases in R&D funding are beneficial for private companies. Unlike government funding, this R&D funding is generally aimed at developing (the D in R&D) or improving products that can then be sold for profit. In an economy driven more and more by new technologies, it seems likely that R&D funding is essential in order for companies to stay ahead of competitors. b. One of the stakeholders for science policy that we identified is universities. Discuss the potential impact on research for students and faculty with the funding trends noted above. Example Response: Researchers working at universities have limited access to industry funding because university research is mostly basic rather than applied. As government R&D funding decreases, the pool of resources available to academic researchers shrinks. Since there has not been a corresponding decrease in the number of university-affiliated researchers, this means that competition for grants and other funding sources becomes greater and greater. It also means that fewer will ultimately receive funding and those that do may receive less money and/or resources. And, there are reduced resources to help fund student research as part of their education.

4. (6 pts). The Equation. Let’s explore the requirements on a rocket needed to launch the to the . This equation was first developed by the Russian scientist Tsiolkovsky in the early 20th century. Beginning with Newton’s third law of motion, one can derive the rocket equation in the form = v ln , where is the 𝑚𝑚0 initial mass of the rocket including fuel, is the finalΔ𝑉𝑉 mass 𝑒𝑒after𝑚𝑚 𝑓𝑓the fuel 𝑚𝑚has0 been expended, v is the exhaust velocity relative to the rocket, and is the change of velocity 𝑚𝑚𝑓𝑓 of the rocket. For details on how to derive this equation see e.g., 𝑒𝑒 Δ𝑉𝑉 https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation. a. To go to the Moon, a rocket needs to essentially achieve from the Earth. Using Conservation of Energy (kinetic + potential energy = 0), derive an expression for the escape velocity. If we begin in at 200 km above the Earth’s surface, calculate the needed to escape from the Earth to the Moon.

M = mass of Earth, m = mass of rocketΔ𝑉𝑉 1 = , = 2 2 1𝐾𝐾 𝑃𝑃 𝐺𝐺𝐺𝐺𝐺𝐺 𝐸𝐸 𝑚𝑚𝑣𝑣 𝐸𝐸 = 0 − 2 𝑟𝑟 22 𝐺𝐺𝐺𝐺𝐺𝐺 𝑚𝑚𝑣𝑣 − = 𝑟𝑟 2 𝐺𝐺𝐺𝐺 𝑣𝑣 2 = 𝑟𝑟 𝐺𝐺𝐺𝐺 𝑣𝑣𝑒𝑒𝑒𝑒𝑒𝑒 � To find the𝑟𝑟 needed to reach the moon from low Earth orbit, we just calculate the escape velocity at 200 km above the Earth. Here, r = (radius of earth) + (height Δ𝑉𝑉 above earth) = 6371 km + 200 km = 6571 km, = 5.97 × 10 kg, and = 24 6.67 × 10 . Plugging these values in, we get = 11,000 = 11 3 𝑀𝑀 𝐺𝐺 −11 𝑚𝑚 𝑚𝑚 𝑘𝑘𝑘𝑘 2 𝑘𝑘𝑘𝑘 𝑠𝑠 𝑠𝑠 𝑠𝑠 b. Going back to the Rocket Equation, calculate the fraction𝛥𝛥𝛥𝛥 of the initial rocket mass that must be dedicated to fuel to go from the Earth to the Moon. Assume v is 4500

m/s, which is typical for a chemical propulsion rocket. 𝑒𝑒 Plugging these values into the rocket equation, we find that

= / = / = 11.5 𝑚𝑚0 𝛥𝛥𝛥𝛥 𝑣𝑣𝑒𝑒 11000 4500 𝑒𝑒 𝑒𝑒 𝑚𝑚𝑓𝑓 The initial mass of the rocket, , is really the mass of the empty rocket plus the mass of the fuel. We need to find the fraction of the initial mass dedicated to fuel, 𝑚𝑚0 which is given by . 𝑚𝑚𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 0 = + 𝑚𝑚 = 11.5 = 11.5 = 10.5 𝑚𝑚0 𝑚𝑚𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑚𝑚𝑓𝑓 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑚𝑚𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 10.5 10.5 = = = = 0.913 + 10.5 + 11.5 𝑚𝑚𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 The𝑚𝑚 0initial𝑚𝑚 rocket𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 mass𝑚𝑚𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟must𝑟𝑟 be 91%𝑚𝑚 𝑟𝑟𝑟𝑟fuel𝑟𝑟𝑟𝑟𝑟𝑟 (!).𝑟𝑟 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 c. Using the mass of the Moon, do this same calculation on the fraction of initial rocket mass needed for fuel to escape from the Moon starting off at 100 km above the Moon’s surface. What conclusions can you draw regarding the relative economics of bringing materials into space manufactured on Earth versus manufactured on the Moon.

2(6.67 × 10 )(7.35 × 10 ) = = 2,310 = 2.31 (1737− 11 + 100 )22 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 𝑚𝑚 𝛥𝛥𝛥𝛥 � The escape velocity from𝑘𝑘𝑘𝑘 the Moon𝑘𝑘𝑘𝑘 is much less than the𝑠𝑠 Earth. This𝑠𝑠 means that it is much more efficient to transport materials from the Moon (escape velocity is only 21% of that needed to escape Earth, and so less fuel is required), if possible, rather than on Earth.