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I wake up screaming into the void, when I see the Earth almost touching me but going away from me at 11.2 $km/s$.

I don't remember what happened before I woke up. I faintly recollect being cannoned up at 11.2 $km/s$.

After waiting forever, the Earth comes to a stop at infinity. Separated by an infinite distance feels very sad, but at least we gained $GM_Em/R_E=3.12*10^{9}$ joules of gravitational potential energy. I cannot explain it but I have always had a thing for gravitational potential energy.

Imagine my horror when I learn that the Earth lost a huge amount of kinetic energy: $0.5M_E(11200)^2=3.75*10^{32}$ joules.

With an ode to Earth's sacrifice, I wonder where did all that energy go? I always thought the Earth's loss of kinetic energy will become our gain of gravitational potential energy.

Could the experts here please help me in finding closure?

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  • $\begingroup$ It seems you just consider earth, sun and you in the universe ? so the earth startet out with negativ potential energy , now has 0 potential energy . and lots of kinetic, it will fall back towards the sun and arrive with negative potential energy , and all its kinetic energy back. How did you escape the pull of earth, why are you not still beside it? $\endgroup$
    – trula
    Commented Dec 26, 2022 at 15:24
  • $\begingroup$ Your question is a little unclear. Are you asking why KE is frame-dependent? If so, we have numerous questions on that topic. $\endgroup$
    – PM 2Ring
    Commented Dec 26, 2022 at 16:03
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    $\begingroup$ I'm not sure why this question is attracting downvotes. Perhaps some readers don't approve of the humorous framing device. Or maybe they feel that you should include some evidence of prior research, eg links to related questions, explaining why the existing answers to those questions are insufficient. $\endgroup$
    – PM 2Ring
    Commented Dec 26, 2022 at 16:05
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    $\begingroup$ Unfortunately your attempt at humor makes your question difficult to parse, and screens out the actual question. Also, you don't explain how you get the results you have, so we can't actually point out any flaw in your reasoning. $\endgroup$
    – Miyase
    Commented Dec 26, 2022 at 16:43
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    $\begingroup$ Voting to reopen. It is clearly wrong to say that the question needs details or clarity when there is an excellent, accepted and upvoted answer below ! $\endgroup$
    – gandalf61
    Commented Jul 9 at 10:54

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I think when you say the Earth starts with a huge kinetic energy in your reference frame, you are referring to an inertial frame that is co-moving with you just after launch. In this frame, at that moment, the Earth is moving very fast, and so yes, has a large kinetic energy.

I think your misconception is that an infinite time later, this motion will cease, and the kinetic energy of the Earth will be zero. This is not the case. You and the Earth will be stationary relative to each other, but will both be moving with almost exactly the same velocity as the Earth had to start with. The kinetic energy of the Earth hardly changes at all.

Perhaps though, you are not referring to that reference frame, but rather to a non-inertial one that remains fixed to you as you accelerate under the influence of Earth's gravity. If that's the case, the misconception is that energy should be conserved in a non-inertial reference frame. The kinetic energy of all the stuff in the universe changes when you view it from a non-inertial frame.

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  • $\begingroup$ Good answer, +1. The OP is not clear, but you seem to have answered all possible intended meanings, thus overcoming an unclear question through a broad answer $\endgroup$
    – Dale
    Commented Dec 26, 2022 at 19:11
  • $\begingroup$ Thank you so much. Both 2nd and 3rd para are educative and the 2nd is even enlightening to me. Originally when I asked the question, my frame was attached to me since it is me who is looking at the Earth both initially and finally. I believe this is also clear in the question. A few hours of pondering over the problem after posting the question, I did realise that my frame isn't inertial and so energy won't be conserved. So, I did arrive at the 3rd para myself. But I still wanted to know how it would look from a 3rd inertial frame, which you clarified very well in your 2nd para. Thanks again! $\endgroup$
    – Ritesh Singh
    Commented Dec 27, 2022 at 3:16