Astronomy and Critical Thinking:

You are standing within a small town on the east coast of the United States looking westward, with one big difference from normal reality:

Instead of the spherical Earth giving you a horizon, the view curves gently upward, allowing you to look out across the whole country. You have the use of a camera (that can measure brightness) and a telescope (that can measure angles), and you can make observations day or night. You can measure distance within the town by pacing.

Your task is to measure the size of the United States without leaving the small town. Provide a detailed procedure and explanation using only the tools and information provided that would accomplish the assignment to estimate the size of the United States. Your explanation must include any assumptions, limitations (constraints), and potential sources of error.

• 2. Physical Reasoning:
• You are the CEO of a company that develops complex spectroscopes and an inventor has proposed the following invention for your consideration:  In order to improve the profitability of your product line, he claims that he can develop an optical system which would focus all the light from large lamp filament into an image of the filament which is smaller and hotter. Using this new design, your company can then purchase low cost filament lamps that could replace the much higher cost small filament high temperature lamps.
• Is this invention at odds with any basic law of physics? Explain your reasoning.
• Assuming the proposed optical design is feasible, are there other technical and/or business questions that must be asked before agreeing to fund the development program? List three critical questions and explain why it is important. (Non-specific generic questions concerning pricing, time to complete etc. will earn minimal credit)