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Gravitational potential energy is inversely proportional to distance: $$V = G\frac{ m_1 m_2 }{d}.$$ when an asteroid is extremely far from earth, its gravitational potential energy (relative to earth) is tiny. If and when it eventually collides with earth (due to earth’s gravitational pull), the kinetic energy converted to heat is substantial. There has been a great increase in energy. Where did the extra energy come from? –

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    $\begingroup$ It come from the conversion of the potential gravitational energy of the asteroid. $\endgroup$
    – xpsf
    Dec 7, 2020 at 18:22
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    $\begingroup$ Gravitational PE is negative. Your formula is missing a negative sign. $\endgroup$
    – G. Smith
    Dec 7, 2020 at 18:24
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    $\begingroup$ Other than the right answers given below, I would like to point out that the term the gravitational potential energy of the asteroid is quite misleading and things start to fall into place pretty easily when you stop using that misnomer. In the above scenerio, the PE is that of the earth-asteroid system, not of the asteroid itself. When defining potential energy of a system, you talk about the internal forces of the whole system, not the external force on one part of the system. $\endgroup$
    – Physiker
    Dec 7, 2020 at 18:40

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when an asteroid is extremely far from earth, its gravitational potential energy (relative to earth) is tiny

Tiny compared to what? If we compare it to the asteroid close to earth, that configuration is the much more energetic configuration. This reduction in potential energy is what is converted into kinetic energy.

The standard description of GPE sets the zero point at infinity, so that closer configurations are marked with a negative energy. But this is just a convention. The important thing is the difference. The distant asteroid has much more potential energy than the close asteroid.

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There has been a great increase in energy. Where did the extra energy come from?

The energy came from "that" which has separated Earth from the asteroid to begin with.

Because from the moment that Earth and the asteroid are separate, the energy is already stored in this Earth-asteroid system as gravitational potential energy and waiting to be released. Stored in the gravitational field set up by the Earth-ateroid configuration. "Whoever" or "whichever" made this configuration, this is where the energy came from originally.

Think of a spring. When elongated, elastic potential energy is stored. As the ends are getting closer, this energy is released (converted into kinetic energy of the moving spring material in this case). Where did the energy come from to begin with? It came from whoever initially stretched the spring by forcing the ends apart. This person or this event did work on the spring, which was then stored in the elongated spring.

Same for any gravitational potential energy between any celestial objects.

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