# 1. Astronomical Data Analysis: (4 points) Below are two data plots for a population of recently discovered extrasolar planets: Graph 1: Graph 2: A. Is it possible that earth-like planets may be more prevalent than shown in this data set? Why? B. Explain the clustered distribution of exoplanets evident on both graphs. C. Which observational technique was used to discover the exoplanets depicted in the two graphs. Explain the technique. D. Graph 2 is inconsistent with theories of solar system formation…Explain why. 2. Physical Reasoning: (4 points) A scientist is completely isolated inside a smoothly-moving box that travels in a straight line through space, and another scientist is completely isolated in another box that is spinning smoothly in space. Each scientist may have all the scientific instruments she likes in her box for detecting her motion in space. What will the two scientists discover after they perform measurements with their scientific instruments. Explain why. 3. Physical Reasoning: (4 points) A. A person weighs 50kg when measured on a typical bathroom scale located in Boston. He enters a deep cave on vacation and stands on the same type of scale. Does anything change? B. If the cave extended to the center of the earth, what would the scale measure at the center of the earth? Explain your answer. C. Qualitatively plot a graph depicting strength of gravity from the center of the earth to the moon. 4. Qualitative reasoning (4 points) Over a century ago, J. C. Maxwell calculated that if Saturn’s rings were cut from a piece of thin sheet metal they would not be strong enough to withstand tidal tension or gravitational gradient tension that Saturn would put on them and would, therefore, rip apart. But suppose the rings were cut from a piece of thick plate rather than thin–sheet. A. Would the thick plate hold? Explain. B. Does it make a difference if the metal rings orbit (spin) around Saturn? Explain. 5. Physical Reasoning: (5 points) You are a manager of a venture capital fund and an inventor has pitched the following invention for your consideration…In order to improve the profitability of an optical product, 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, the company can then purchase low cost filament lamps that could replace the much higher cost small filament high temperature lamps. A. Is this invention at odds with any basic law of physics? Explain your reasoning. B. If the proposed optical design works, are there other business questions that must be asked before agreeing to fund the development program? List the questions and explain WHY it is important. 6. Astronomy (4 points) A. How might the presence of intergalactic dust as an agent for reddening and dimming the light from ever more distant galaxies affect the determination of galactic distances assuming that galaxies all have the same brightness? B. How might the presence of intergalactic dust as an agent for reddening and dimming the light from ever more distant galaxies affect the determination of galactic distances using the redshift associated with the expansion of the cosmos?

1. Astronomical Data Analysis: (4 points)
Below are two data plots for a population of recently discovered extrasolar planets:
Graph 1:

Graph 2:

A. Is it possible that earth-like planets may be more prevalent than shown in this data set? Why?
B. Explain the clustered distribution of exoplanets evident on both graphs.
C. Which observational technique was used to discover the exoplanets depicted in the two graphs. Explain the technique.
D. Graph 2 is inconsistent with theories of solar system formation…Explain why.

2. Physical Reasoning: (4 points)
A scientist is completely isolated inside a smoothly-moving box that travels in a straight line through space, and another scientist is completely isolated in another box that is spinning smoothly in space. Each scientist may have all the scientific instruments she likes in her box for detecting her motion in space. What will the two scientists discover after they perform measurements with their scientific instruments. Explain why.

3. Physical Reasoning: (4 points)
A. A person weighs 50kg when measured on a typical bathroom scale located in Boston. He enters a deep cave on vacation and stands on the same type of scale. Does anything change?
B. If the cave extended to the center of the earth, what would the scale measure at the center of the earth? Explain your answer.
C. Qualitatively plot a graph depicting strength of gravity from the center of the earth to the moon.

4. Qualitative reasoning (4 points)
Over a century ago, J. C. Maxwell calculated that if Saturn’s rings were cut from a piece of thin sheet metal they would not be strong enough to withstand tidal tension or gravitational gradient tension that Saturn would put on them and would, therefore, rip apart. But suppose the rings were cut from a piece of thick plate rather than thin–sheet.
A. Would the thick plate hold? Explain.
B. Does it make a difference if the metal rings orbit (spin) around Saturn? Explain.
5. Physical Reasoning: (5 points)
You are a manager of a venture capital fund and an inventor has pitched the following invention for your consideration…In order to improve the profitability of an optical product, 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, the company can then purchase low cost filament lamps that could replace the much higher cost small filament high temperature lamps.
A. Is this invention at odds with any basic law of physics? Explain your reasoning.
B. If the proposed optical design works, are there other business questions that must be asked before agreeing to fund the development program? List the questions and explain WHY it is important.

6. Astronomy (4 points)
A. How might the presence of intergalactic dust as an agent for reddening and dimming the light from ever more distant galaxies affect the determination of galactic distances assuming that galaxies all have the same brightness?
B. How might the presence of intergalactic dust as an agent for reddening and dimming the light from ever more distant galaxies affect the determination of galactic distances using the redshift associated with the expansion of the cosmos?