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When @anna v explained why the planetary model of the atom does not make sense in this post, she said the electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus.

However, when the Earth orbits the Sun, isn't it accelerating continuously toward the Sun? If this is the case, should the Earth radiate away its energy via gravitons and fall into the Sun eventually?

I also checked questions about Why doesn't the Moon fall onto the Earth?, but the answers didn't talk about radiating away gravitons.

Qmechanic
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戴淯琮 Yu-Tsung Tai
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1 Answers1

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The earth stores a very large amount of energy, and very little is lost in gravitational waves. According to the Wikipedia article on gravitational waves, the orbital energy amounts to $1.14*10^{36}J$ and only $200J$ is lost every second. Hence, for the earth to lose 1% of its orbital energy would take about $5*10^{31}s$, or more than $10^{24}$ years. As the universe is of the order of $10^{10}$ years old, that 1% loss would take about 100 trillion times longer than the age of the universe - and about 300 trillion times longer than the age of the earth.

In other words, the loss is negligible.

hdhondt
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