As time progresses, which scenario will happen first? The moon colliding with Earth, or the Earth colliding with the Sun? I figure the Moon and Earth will happen first, based on proximity, but the sun has a much larger gravitational pull. I am not a Physicist, but I am a geologist in graduate school, so I have a great appreciation/understanding for large forces, time and math. I am very curious and would like to get pointed in the right direction mathematically for this question, as well as, the correct answer :-). Thank you.
As the moon is continually receding from the earth due to the tides, the end result will be a stable orbit.
about 2.3 billion years from now, the increase of the Sun's radiation will have caused the Earth's oceans to vaporize, removing the bulk of the tidal friction and acceleration.
The orbit should be stable.
But the sun will finally become a red giant
Earth is not expected to survive the Sun's transition into a red giant. At its largest, the Sun will have a maximum radius beyond Earth's current orbit, 1 AU (1.5×1011 m), 250 times the present radius of the Sun. By the time the Sun has entered the asymptotic red giant branch, the orbits of the planets will have drifted outwards due to a loss of roughly 30% of the Sun's present mass. Most of this mass will be lost as the solar wind increases. Also, tidal acceleration will help boost Earth to a higher orbit (similar to what Earth does to the Moon). If it were only for this, Earth would probably remain outside the Sun. However, current research suggests that after the Sun becomes a red giant, Earth will be pulled in owing to tidal deceleration.
So it is not that simple, because it depends on orbits and rotational velocities etc, so models have to be used and it is still a topic of research:
According to these solar evolution models, the closest encounter of planet Earth with the solar cool giant photosphere will occur during the tip-RGB phase. During this critical episode, for each time-step of the evolution model, we consider the loss of orbital angular momentum suffered by planet Earth from tidal interaction with the giant Sun, as well as dynamical drag in the lower chromosphere. We find that planet Earth will not be able to escape engulfment, despite the positive effect of solar mass-loss. In order to survive the solar tip-RGB phase, any hypothetical planet would require a present-day minimum orbital radius of about 1.15 AU.