# Gravitational force between Earth and Sun is decreasing

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?

• 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. Jun 25, 2016 at 1:02
• 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 Jun 25, 2016 at 4:23
• 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. Jun 25, 2016 at 6:17
• 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! Jun 25, 2016 at 7:06
• Possible duplicates: physics.stackexchange.com/q/208/2451 , physics.stackexchange.com/q/114735/2451 and links therein. Jun 25, 2016 at 13:36

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.