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Notes:
NASA has stated that it would like to travel to the last planet remaining unvisited. It took Voyager around 16 years to make it to the orbit of Pluto, though Pluto missed the appointment. Now, 24 years later, it would seem that we should be able to arrive at Pluto much faster, so I have arbitrarily selected a 10x faster trip, or 1.6 years. Well it is easy enough to calculate the speed needed, we take the (average) orbital distance to Pluto, and divide by the number of seconds in 1.6 years, to get an average speed of about 100 km/s. This is the change in velocity needed in the rocket equation. Then selecting various specific impulses, Isp, we find that the ratio of the mass of the rocket to the mass of the payload is as given in the table. Note that a “good” Isp of around 10,000, permits a reasonably sized payload to make it to Pluto in 1.6 years. I’m glossing over another problem, of course, that high Isp rockets are generally energy starved, and would need a small nuclear reactor to provide the power for the thrust. But since everything to date has been launched by chemical rockeds, and even advanced chemical fuels will not exceed 400s of Isp, it should be clear that if we are in a hurry, we can’t get anything to Pluto much larger than a pencil eraser.