Suppose we invent a unit of mass which we shall call the cavendish \( (C) \). One cavendish of m...

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Suppose we invent a unit of mass which we shall call the cavendish \( (C) \). One cavendish of mass is defined such that \( G=1.0000(A U)^{3} /\left(y r^{2} \mathrm{C}\right) \). Our unit of length is the astronomical unit \( (A U) \), the earth-sun distance \( -1 A U=1.496 \times 10^{11} \mathrm{~m} \) - and our unit of time is the year \( (y r) \). (a) Determine the conversion factor between \( C \) and \( \mathrm{kg} \). (b) Find the mass of the sun in \( C \).
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