[jerrygg38 (OP)]

Does the earth move away from the sun when it slows down?
   The equations are:
GMeMs/R^2   = Me[V^2]/R
RV^2  = G Ms
   It appears that if V decreases the distance R increases. Likewise if V increases the distance R decreases.
   These are steady state equations. It appears to me that over time the Earth will slow and strangely this will cause it to move away from the sun instead of heading right toward the sun.
   If we get hit by a comet we could slow or speed up depending on whether the comet hit us opposite to the direction of motion or with the direction of motion. The comet would add mass so the problem is more complex.
  Does anyone know what really happens?

[evan_au]

This was worked out by Kepler, when he worked out that the planets follow ellipses around the Sun.
- The orbit sweeps out equal areas in equal time (Kepler's second law)
- When the planet is closest to the Sun (as the Earth is in January), it travels the fastest, making it swing out farther in February
- When the planet is farthest from the Sun (as the Earth is in July), it travels the slowest, making it fall in towards the Sun in August

Isaac Newton proved mathematically that only an inverse square law of gravitation can explain these orbits.

See: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

[jerrygg38 (OP)]

Thanks for all the information. For simplicity I always look at a circular orbit even though I know it is an ellipse. So I see now that the radius and velocity constantly change.
   I am still a little confused what happens if the Earth get hit by a very large meteor. Would that change the orbit due to the momentum and total  mass or is the orbit change only dependent upon the combined mass of the Earth and meteor?
   In addition does the Earth slowly drift away from the sun. I believe the science programs on tv say the moon is receding from us at a one inch per year rate. Are we receding from the sun?

[evan_au]

I am still a little confused what happens if the Earth get hit by a very large meteor. Would that change the orbit due to the momentum and total  mass or is the orbit change only dependent upon the combined mass of the Earth and meteor?

It would have to be a very big meteor to make a difference. And we would not be around to report on it.

The dinosaur-killer asteroid is thought to be about 10km across, compared to Earth's 12000 km. That makes it about 1 billionth the mass of the Earth, so it would have made negligible difference to Earth's orbit.

Small tugs over a longer period do have a significant impact - the gravitational tugs of Jupiter and Saturn distort Earth's orbit slowly over time, changing the eccentricity. This has been linked to the start of ice ages on Earth.
See: https://en.wikipedia.org/wiki/Milankovitch_cycles

In addition does the Earth slowly drift away from the sun. I believe the science programs on tv say the moon is receding from us at a one inch per year rate. Are we receding from the sun?

It is expected that as the Sun enters its Red Giant phase, it will lose a lot of its outer envelope as a planetary nebula, reducing its mass, and allowing Earth to swing out farther on its orbit. But surface life would be toast.

At present, the Sun is losing mass through its solar wind, and gaining mass by the various comets and asteroids that crash into it. I'm not sure which effect is winning, but the effects are small. So the Sun's mass is not making dramatic changes to Earth's orbit at present.

[jerrygg38 (OP)]

Thanks for the information. I see it is a huge scientific problem for specialists in the field.