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I was thinking about the Google XPrize for Space Travel the other day.

In order to claim the prize of building a robot that goes to the moon, travels 500m, and relays data, I had the idea of building a tiny vessel the size of a marble and shooting it at the moon with a railgun.

The theory is that since the mass of the marble-sized craft is only a fraction of the size of a regular shuttle, it should take exponentially less energy to get it to the moon.

So, if you could aim it right, and shoot it with enough power to escape Earth's gravity (Let's say it weight 1oz) couldn't you shoot your own vessel to the moon with essentially a potato launcher?

Why does this not work?

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    $\begingroup$ Very related: physics.stackexchange.com/questions/88145/… $\endgroup$ – Kyle Kanos May 5 '14 at 19:53
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    $\begingroup$ If you simply throw something up, it needs to overcome gravity as well as push all the air out of the way. There's a lot of air in any trajectory towards space. Even for a marble. $\endgroup$ – Keep these mind May 5 '14 at 19:53
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The advantage of launching a large rocket is the following: you can carry fuel on the craft so that you can produce the required kinetic energy to over come Earth's gravitation and air resistance to escape the gravitational hold of the planet. This can be done over a long period of time or height in the atmosphere so that your speed is initially low then increases as you burn more fuel. Since the force of air resistance is proportional to speed squared and also proportional to air pressure, it's much more efficient to have a low speed near the ground and then increase the speed when higher up.

Shooting a marble is the opposite. You reach the maximum speed at the point of exit from your rail gun device. The escape velocity at sea level is 11km/s, but this is without air resistive losses. You would need to be even faster at the exit of the muzzle/rail gun if you take this into account. A look on wikipedia tells me that the fastest military rail guns can only do 2km/s.

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You noticed that smaller (less massive) object would have a lot less potential energy up there. And you conclude that you could give enough kinetic energy right at the start and throw it up to moon. Yes, you could overcome the gravity like that.

However, the potential force (gravity) is only one side of the coin. As the object gets smaller, the surface forces (drag) decreases quadratically thus getting relatively bigger compared to volume forces like inertia* and gravity which where the only forces you noticed. And you would not overcome drag forces.

This would mean two effects. Firstly it would need faster and faster velocity as you decrease the size as it's inertia will be weaker compared to drag. But even worse is the side-effect of drag. Literally side-effects. Your marble would just get blown away. Even if you make it fly off into space, chance to hit moon will be tiny.

Similar situation can be seen in the bacterial world - they are so small that their physics are dominated by drag forces - there is no inertia and they can't swim in the way like the fish does.

  • Read the comments. Inertia is not an actual force, but it is useful to refer inertia as one in this case.
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  • $\begingroup$ "As the object gets smaller, the surface forces (drag) gets relatively bigger." No, AFAIK, drag force is approximately proportional to surface area. $\endgroup$ – Shivam Sarodia May 5 '14 at 22:18
  • $\begingroup$ @Draksis The volume decreases faster than area so surface forces get relatively bigger compared to volume forces like gravity and inertia. $\endgroup$ – Džuris May 6 '14 at 7:50
  • $\begingroup$ All right, I see what you mean. However, you should clarify this in your original answer. Also, note that inertia is not a force. $\endgroup$ – Shivam Sarodia May 6 '14 at 16:31
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    $\begingroup$ @Draksis Thanks, I will clarify it. While inertia is not a true force it is sometimes (fluid dynamics useful to refer to it as a force. For example Navier-Stokes equation can be seen as balance of inertial force and pressure, viscuous and other body forces. $\endgroup$ – Džuris May 6 '14 at 18:56
  • $\begingroup$ That's a fair point. I felt like it was important to bring up, though, since non-physicists often think of inertia as a true force. $\endgroup$ – Shivam Sarodia May 7 '14 at 19:23

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