Based on the HW scenario provided and previous HW problems, answer the questions below. $$You may work with other students currently enrolled in this course but each student must submit their own handwritten solution to parts $1$ and $2.$You may type your answers for the remaining parts of this problem. $$Solutions to mathematical problems should state all given values, show all equations and list any constants used. $$To receive full credit you must SHOW your work. $$Remember to label the units for each numerical answer. $$Providing an equation and an answer alone is not sufficient.

$6.$ A spacecraft visible sensor operating at $0\mathrm{.}5$m with a nadirresolution of $0\mathrm{.}61$ m should satisfy Quicklook mission requirements.

$6\mathrm{.}1$ Using the mission orbit assumed in Question $3,$ calculate the sensor aperture diameter necessary to meet the above resolution requirement.

$6\mathrm{.}2$ Using the following nominal values from an existing spacecraft sensor: Aperture Diameter $=0\mathrm{.}70$ m; Mass $=200$ kg$,$ Size $=1\mathrm{.}9$m length x $1\mathrm{.}5$m diameter; peak power $=420$W$,$ estimate the Quicklook sensor mass, dimensions and peak power using the scaling techniques presented in this course.

$6\mathrm{.}3$ Using your sensor mass and power results From $6\mathrm{.}2$ and appropriate course reference, generate an initial dry mass and power budget for each bus subsystem $($ Power, ADACS, TT&C$,$ Thermal, Propulsion, Structure$)$ with no margin.

$6\mathrm{.}4$ For a Phase$-$A design, what would be the estimated spacecraft dry mass with margin?

$6\mathrm{.}5$ Explain the importance of margin in spacecraft design.

$6\mathrm{.}6$ How would a smaller nadir resolution of $0\mathrm{.}5$ affect Swath Width$/$coverage$?$ Would more or fewer spacecraft be required in the QL constellation to provide the needed coverage?$$ Discuss your conclusions.