what is the distance between the Sun center and the two foci of the Earth orbit?

[Myth27]

I'm having a hard time finding this information on google, most places say it's very close. How much? are the two focus inside the Sun ?

[Rakaydos]

One of the foci definitely is, as by definition for elliptical orbits.

If the Earth's eccentricity was zero, that would mean it was a circular orbit, and therefore both foci would be at the same place. Therefore the distance between the foci is related to the centricity so you might look in that direction.

[jayem]

One of the foci definitely is, as by definition for elliptical orbits.

If the Earth's eccentricity was zero, that would mean it was a circular orbit, and therefore both foci would be at the same place. Therefore the distance between the foci is related to the centricity so you might look in that direction.

Or is you want to skip the explicit reference to eccentricity, look at the maximum and minimum distance of earth to the sun.

[factotum]

One of the foci definitely is, as by definition for elliptical orbits.

Not necessarily--one of the foci is at the *barycentre* (e.g. the centre of mass) of the pair of bodies you're considering, which is not always inside either of them; it definitely isn't for the Pluto-Charon system, for instance, and neither is it true for the Sun and Jupiter (the barycentre for that is a few tens of thousands of kilometres above the Sun's surface).

You can calculate how far apart the two foci of the orbit are from the eccentricity and the semi-major axis--in the case of Earth this is 149.6 million kilometres and 0.0167, so the distance between the foci is 2 x 149.6 million x 0.0167, or about 5 million kilometres, which is much larger than the Sun's diameter; therefore, both foci cannot be inside the star no matter where they are. (I believe Kepler may have originally proved this and not been very happy about it, but I'm unable to find confirmation of that).

[Mastikator]

Okay so the Earth's periapsis (the lowest point of the orbit) is 147,098,074 km and apoapsis (the highest point of the orbit) is 152,097,701 km.

The average of these is 149,597,887.5 km (which is 1 AU to the precision of 1 in 1,000,000)

Does that answer your question?

[Tvtyrant]

I thought the sun/earth barycentre was just inside the skin of the sun. That was how solar flares were explained in my highschool course, the sun's tides were so extreme that it caused geysers when gravitation pulls hit right.

[DeTess]

I thought the sun/earth barycentre was just inside the skin of the sun. That was how solar flares were explained in my highschool course, the sun's tides were so extreme that it caused geysers when gravitation pulls hit right.

No, that's probably the sun-jupiter barycentre (or, since it's talking about the dynamics of the sun, probably the barycentre of the entire solar system). The mass of the earth is negligible compared to that of the sun, so the barycentre is only off from the sun's centre by about 500 km. See this wikipedia page for the math: https://en.wikipedia.org/wiki/Barycenter

[Myth27]

Thank you Guys