Simulating Jules Verne Earth to the Moon trip?

[riveay]

Has anybody attempted simulating the trip to the moon described by Jules Verne?

I've done a bit of research and found this two posts:

https://www.physicsforums.com/threads/showing-deadly-acceleration.909104/#post-5726115

https://www.physicsforums.com/threa...ship-fired-from-a-cannon.793891/#post-4985868

The first one says that it is impossible for the human body to withstand the acceleration and the second one a quick calculation of the acceleration within the cannon.

Now, has anybody attempted to simulate this considering the gravity gradient and the orbits? I know that Jules Verne made some mistakes due the knowledge current at the time he wrote the book, but still, I find it insteresting to try it out.

The factors I know are required for the simulation are:

• Distance to the moon
• Muzzle velocity
• Gravity as a function of time
• Air drag (maybe neglect it for simplicity's sake?)

Please, do let me know if I'm missing something.

Thank you very much to all! :)

 

[Vanadium 50]

Can you explain what you mean by simulating?

 

[riveay]

Can you explain what you mean by simulating?

Using the values from the book in a programme and calculating the time, deceleration and how close to the moon it would get.

 

[Vanadium 50]

Ah. This is more "calculating" than "simulating".

 

[riveay]

Ah. This is more "calculating" than "simulating".

I used the wrong word there. I apologise.

So, I would really like to know how to calculate how close a project like that would be from the moon. Assuming, of course, that the people inside the capsule would resist the acceleration. I'm quite new to aerospace and more so to ballistics. I understand that the capsule is accelerated by the gas expansion whilst it inside tha cannon, but I don't have any knowledge on which formulas to use to calculate such acceleration and then, how to calculate the change in velocity due to the gravity, drag force and whatever forces I'm missing.

Any hints?

 

[Charles Link]

I studied this a little when I was in high school, and I also read the book. Jules Verne did have an uncle who I believe was a mathematics professor, so some of his science-fiction was based on actual calculations. I believe there is one place in the book where they give the result of where the point of zero gravity occurs between the Earth and moon=I believe it is at 9/10 of the distance to the moon, because the Mass of the Earth is 81x that of the moon. Anyway, if I'm not mistaken, he got that part correct. $\\$ Editing: A quick google is unable to confirm the math professor uncle, but I researched this topic when I was in high school in 1973, and that was what they said, if I remember, in some kind of biographical write-up that I found.

 

[DrStupid]

Ah. This is more "calculating" than "simulating".

Isn't it an n-body simulation (with n=3)?

 

[Janus]

I used the wrong word there. I apologise.

So, I would really like to know how to calculate how close a project like that would be from the moon. Assuming, of course, that the people inside the capsule would resist the acceleration. I'm quite new to aerospace and more so to ballistics. I understand that the capsule is accelerated by the gas expansion whilst it inside tha cannon, but I don't have any knowledge on which formulas to use to calculate such acceleration and then, how to calculate the change in velocity due to the gravity, drag force and whatever forces I'm missing.

Any hints?

The most difficult part of this would be calculating the total effect of drag. It is dependent on the shape of your projectile, its cross-section area, the density of the air, and the velocity of the projectile. Only the first two would be constant during the passage through the atmosphere.
The values I got from my copy of the book were 20,000 lbs for the weight of the projectile and a diameter of 9 feet. It was fired with a velocity of 36,000 ft per sec.
With no atmospheric drag, this velocity only get you ~ 46% of the way to the Moon. You'd need ~ 378.4 ft/sec in additional muzzle velocity to reach the Moon.
Granted, the rotation of the Earth will give the projectile a bit of an extra boost. At the latitude of the launch the tangential velocity of the Earth's surface is ~1354 ft.sec. However, this would be applied at a right angle to the cannons bore, so would only add ~25 ft/sec to the projectiles velocity.