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I was trying out a simulation about escape velocity to understand why direction has no impact on it here :http://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Escape_Nav.swf::Escape%20Velocity%20Interactive

I understand that gravitational fields should be conservative, that is, getting from one equipotential line to another should require the same amount of energy no matter the path taken. That's what surprised me about this simulation (pictured below) enter image description here

The "bottom" rocket (orange) was launched horizontally from earth whilst the "top" rocket (yellow) was launched vertically from earth at the same speed (exactly escape velocity). I would expect that for the same distance away, both rockets should have the same speed. What I'm not getting, is that the bottom rocket (orange) is both further away from earth AND has greater velocity (and hence energy) than the top rocket (yellow).

This to me seemingly tells me that the conservative nature of gravity is violated as it seems like it does depend on the path taken? Could someone please tell me where my interpretation is falling short?

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  • $\begingroup$ Were they launched at the same speed? Does this simulation take the rotation of the earth into account? Assuming the simulation isn't broken it must be that the rockets somehow did not start with the same energy, or you are misinterpreting the output of the simulation. $\endgroup$ – Aaron Stevens Apr 24 at 2:58
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    $\begingroup$ @AaronStevens I think they are both launched from poles with the same speed: $11.2kms^{-1}$. So in theory the result I'm seeing shouldn't be the case? $\endgroup$ – John Hon Apr 24 at 3:23
  • $\begingroup$ Yeah that's right. I'm on my phone right now so I can't mess around with it on my own. $\endgroup$ – Aaron Stevens Apr 24 at 4:17
  • $\begingroup$ Were the rockets launched from the same location? $\endgroup$ – Mauro Giliberti Apr 24 at 9:43
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I think the key is found in the final paragraph of the "how to" section:

One point to note is that, in reality, if a rocket were fired horizontally at anything less than the escape speed from the surface of a smooth earth, it would immediately impact on the surface. The only way to really complete an orbit, if fired with a speed less than the escape speed, is to be fired from a high altitude. The scale of the graphics here does not allow us to show that.

If you run the simulation at speeds less than the escape velocity, you will find that you can achieve an orbit with the "bottom rocket". Therefore, it must be that the bottom rocket actually starts at a larger distance from the center of the earth compared to the top rocket, thus giving it a larger total energy since the rockets each start with the same speed. This leads to the bottom rocket having a larger total energy, and is why you see that the bottom rocket has a larger speed at a larger distance as well.

Honestly though, there isn't anything definitive we can say without seeing what is going on behind the scenes. It should be noted that your question

This to me seemingly tells me that the conservative nature of gravity is violated as it seems like it does depend on the path taken? Could someone please tell me where my interpretation is falling short?

has an easy answer. Gravity is a conservative force. In reality this cannot be violated. Anything that violates this here is just due to lack of knowledge of how the simulation works, or is an error in the simulation itself.

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