How long (in seconds) does it take for a radio wave of frequency 8.94 × 106 s–1 to reach Mars when Mars is 8.2 × 107 km from Earth?
Answers
To have any effect on the Earth's position in the Solar System, the mass in question would have to be removed from the vicinity of Earth. Mass in Earth orbit is so close to Earth, and its distribution around Earth so uniform, that the gravitational effect on the rest of the Solar System is identical to that mass still being on Earth.
Humanity has removed a few hundred tonnes from the vicinity of Earth since we began this activity in 1959. This in on the order of two or three tonnes per year. The Earth masses six million trillion tonnes. If we assume that removing one millionth of Earth's mass would have a measurable effect on the rest of the Solar System, then at the present rate, we would achieve this effect in ((six million trillion * one millionth) / three) = two trillion years. Two trillion years is hundreds of times longer than the expected remaining lifetime of the Sun.