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In 'Tom Swift and his Cosmotron Express' (1970) by Victor Appleton II, Tom invents his fastest spaceship that can go to the moon in 3 hours and tour all the planets in the solar system in 2.5-3 days. It claims to be able to do this by being able to accelerate continuously. Has anyone done the math to figure out what acceleration would be needed to do this? The book says it is many gravities but doesn't say how many. I assume you have to accelerate for the first half the voyage and decelerate for the second half.

Thank you for the excellent answers below (1.3g for moon, 500+ g for tour of solar system) and some excellent Tom Swift and Tom Swift, Jr references at:

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@WayfaringStranger's answer is excellent, but let's talk about the other part of the question - 2.5 to 3 days to tour all the planets of the solar system, using a constant acceleration of 13.18 meters per second squared.

The exact time would depend on the positions of the planets at the time of the trip. However, considering the orbital periods of the planets (88 days for Mercury), the planets will be reasonably stationary with respect to each other over a time period that short. As a result, every leg will be a direct, straight line path.

I used The Planets Today to look at the current relative positions and mapped out a rough guess at a "best" itinerary (Earth - Jupiter - Uranus - Neptune - Mars - Mercury - Venus - Saturn - Pluto) then used Wolfram Alpha to get the current distances between the planets and threw together a crude spreadsheet to calculate travel times at the given acceleration and got a total figure of 1458 hours (nearly 61 days). It would take more than 500 gravities to get this number down to 3 days.

Yes, we have to include Pluto because at the time the story was written, Pluto was still considered a planet.

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    "That's some awesome acceleration!" Tom said increasingly swiftly. Commented Dec 28, 2012 at 6:42
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    "was"??? -1 for insinuating that Pluto is not a planet :( Commented Dec 28, 2012 at 12:56
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    @DVK - It isn't my fault that astronomers do not currently classify it as a planet. Commented Dec 28, 2012 at 13:57
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Hyperphysics equations for constant acceleration motion

Average distance from Earth to the Moon is 384,400 km.

Assume first half of trip is constant accel, second half constant decel.

Tom, Bud and likely Chow travel halfway to the moon in 1.5 hours; that's 192,200,000 meters in 5,400 seconds.

Given Y = 0.5 a t^2 and Y = 192,200,000 Then: a = acceleration = 13.18 meters per second squared That's about 1.35 X G, which is short of the 'many' that were claimed, but still a darn good space drive.

Their speed at turnover (v = at) is over 70 km/second.

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