Actually, I think what will happen is will continue moving further away... but before we have complete freedom, the Sun will go nova, and the explosion will expand to us and beyond us, vaporizing us.
And, while on the topic of ellipsis, perihelion and so on, the earth’s orbit varies from elliptical to near-circular, in a 100,000 year cycle driving our ice ages and warm periods. See Milankovitch for more info.
IMHO the Sun’s variability of output and the Milankovitch Cycles explains our climate changing over time...The rest is insignificant by comparison...
I don’t think our sun is big enough to go nova. I thought it was going to be a burn out.