Since the Sun is losing mass, can a planet's orbit change be measured?

[BarnRat]

Since the Sun is changing 4M tons of matter into energy every second and that energy eventually makes its way to the surface and is emitted as an outbound sphere of EM radiation, then the planets' orbits would change over time due to the less massive Sun at the solar system's core. It would seem that there would be a slow outward spiral of each planet. But is this not perceptible by our instruments? Are other factors countering this effect? Does the Sun gain enough mass from interstellar debris that its gravity sucks into make up for the difference in matter-energy change due to the thermonuclear processes at its heart?

 

[Chronos]

Solar mass loss due to hydrogen fusion amounts to about an Earth mass over the past 4.5 billion years. Theoretically, this would cause an increase in Earth orbit of about 7000 miles - as compared to the ~93 million miles we currently enjoy. The effect is obviously insignificant. The sun accretes only a tiny fraction of mass compared to fusion losses so that effect can be essentially ignored. Earth orbit is also affected by tidal drag from the sun. That effect is also relatively miniscule.

 

[BarnRat]

Thank you for the response.