According to one of the most famous equations in physics, i.e. $E=mc^2$, the mass of the Sun is decreasing as it emits energy. So there must be some kind of disturbance in planetary orbits, and if there is, then how will it be according to Newton's perspective and by Einstein's perspective?

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    $\begingroup$ Something I try to drum into my students is the importance of relative scales in physics. Have you worked out how much mass is lost in a year? Hove you looked at what fraction of the current solar mass that represents? Have you then figured what the yearly change in the radius of the Earth's orbit would be on that account? Those are the kinds of question that can lead you to understand this phenomena for yourself. $\endgroup$ – dmckee --- ex-moderator kitten Jun 25 '16 at 1:02
  • $\begingroup$ Thanks for your great suggestion but I'm just a high school student I can't solve Einstein's field equation but yeah I can solve it using Newton's gravitational law $\endgroup$ – Mr. Robot Jun 25 '16 at 4:23
  • $\begingroup$ This is a completely classical Newtonian problem. The sun is losing about 1.5 million metric tons of mass per second due to radiation. Put that in relation to the total mass. $\endgroup$ – CuriousOne Jun 25 '16 at 6:17
  • $\begingroup$ The big effects are all Newtonian, and so you should be able to calculate them for yourself. It is a good exercise. As for Einstein, the Earth-Sun system is emitting gravitational radiation and the Earth is spiralling in towards the Sun and will eventually crash into it. According to en.m.wikipedia.org/wiki/Gravitational_wave we get $10^{-15}$m closer to the Sun every day (about the diameter of a proton) and will crash into it in around $10^{23}$ years. A lot else will have happened long before that! $\endgroup$ – Martin Kochanski Jun 25 '16 at 7:06
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/208/2451 , physics.stackexchange.com/q/114735/2451 and links therein. $\endgroup$ – Qmechanic Jun 25 '16 at 13:36

Yes, the sun's mass isn't constant causing disturbances of orbits, but should you care.

Mass of sun now: $\approx 2 * 10^{30}$ kg so $E \approx 1.8 *10^{47}$ J. Radiation per year is about $10^{34}$ J.

You've got a lot bigger problems that affect your calculation of orbits. Especially like where Jupiter is relative to where you thought it was. Namely the many body problem.


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