Say we wished to use SI units, that is, seconds for the orbital period and meters...

 

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Say we wished to use SI units, that is, seconds for the orbital period and meters for the semimajor axis, instead of years and a.u. We would need one conversion to change the time from years to seconds, and one to change the distance from a.u. to meters, and we would have to raise each to the power of its respective variable in the equation (i or j). If we wished to make this conversion by multiplying only our values for T, instead of having to convert both our T values and our a values, we could combine these two conversion factors into one. If you were to do this, by what factor should you have to multiply the values for the periods? (Note that when you arrive at your conversion factor, you can check it by comparing it to the value that you get if you evaluate K(1/1), by calculating (4)(/), with the values given above for G and M.) How would this have changed the intercept of your log-log graph? What would its value have been? Say we wished to use SI units, that is, seconds for the orbital period and meters for the semimajor axis, instead of years and a.u. We would need one conversion to change the time from years to seconds, and one to change the distance from a.u. to meters, and we would have to raise each to the power of its respective variable in the equation (i or j). If we wished to make this conversion by multiplying only our values for T, instead of having to convert both our T values and our a values, we could combine these two conversion factors into one. If you were to do this, by what factor should you have to multiply the values for the periods? (Note that when you arrive at your conversion factor, you can check it by comparing it to the value that you get if you evaluate K(1/1), by calculating (4)(/), with the values given above for G and M.) How would this have changed the intercept of your log-log graph? What would its value have been?