Orbital Effects of a Significant Mass Increase

[Johmpa]

I've recently been pondering the following thought experiment:

Assume that the Earth was to gain a large amount of mass in a very short time, which effectively increase the mass of the Earth by approx. 1.5 * 10²¹ kg, and this in course of say five years.

What I've been trying to figure out is what effect this would have on the Earths orbit around the Sun and, more interestingly, the Moons orbit around the Earth. Would this sudden increase result in an eventual collision between the Moon and Earth, given Earths increased gravity?

 

[Nabeshin]

For the earth-sun system, an increase on the order of 10^21 kg is almost nothing and barely shifts the center of mass of the system at all, so there would likely be no noticeable effects (small changes in the length of the year, perhaps).

As far as the earth-moon system is concerned, 10^21 kg is only ~.1% of the total mass of the Earth so the increase isn't that appreciable here either. Since gravity scales linearly with mass, this amounts to only a ~.1% change in gravitational force of the Earth on the moon, which likely will not cause any catastrophic effects.

Bottom line: 10^21 kg is not enough to produce huge changes in either of these systems.

 

[Chronos]

Plug variable mass into Keplers Law and see what you get.