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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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.
AHusain
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