# If space is expanding isotropically, then why are distances between objects in the solar system not expanding

As I understand the metric expansion of space, space itself is expanding uniformly, isotropically. Distant light, passing through our solar system expands, as does the distance between atoms on earth. Any matter that is gravitationally bound does not expand, presumably, because gravity compensates by holding everything together, but it must be stretched apart before being held back together by stronger local forces.

So I did the calculations based on the current Hubble constant, and I determined that space everywhere is expanding by about 7% every billion years. So if the space between the sun and earth has expanded 7%, then I would expect it the orbit increase, and the length of a year to be shortened. Problem is, it seems like this is not accounted for in models of earths orbit.

So my question is, does light not expand as it passes through the solar system? And if not, then, how can that be explained in an isotropic universe? My understanding is that it is space that is expanding not the matter within it. If that is true, then I would expect all distances to be affected even between gravitationally bound objects like the sun and earth.

• "Any matter that is gravitationally bound does not expand, presumably, because gravity compensates by holding everything together, " is correct, but it is not clear what you mean by "it must be stretched apart before being held back together by stronger local forces". The answers to these questions may help: "Is the expansion of space universal or local?", "Does gravity keep nearby galaxies from flying apart in space expansion?". Dec 13, 2022 at 2:29
• Thanks David for your quick response, and I need to study the equations in the link that you sent, but my initial thought is they confirm my suggestion that there is a balance between gravity and cosmic expansion. The way that I’m visualizing this is that expansion slowly moves the sun and the earth apart, which increases the potential energy of the earth, changing the period of its orbit, although it remains gravitationally bound. In other words, the stretching of space should increase the potential energy of the earth, or of two galaxies for that matter, since they are further apart gravitat Dec 13, 2022 at 4:27
• So if I can try it one more time, the expansion of space is linear, independent of any gravitational well, so expanding the space within a deep gravitational well, like the sun and earth, will require an input of energy. You could take this to an extreme around the edge of a black hole, where even a small stretching of space could potentially require a huge amount of energy, since some particle would be ever so slightly drawn back from the edge Dec 13, 2022 at 4:41
• @ThomasTiger but, but, but the planetary systemis gravitationally bound. there is no "slowly moves" . The interactions happen instantaneously and the expansion is not felt by the gravitational interaction. Dec 13, 2022 at 5:24
• I think this is a duplicate of Why does space expansion not expand matter?, but almost all of the answers to it are wrong, except for this one. See also this answer and this article. Dec 13, 2022 at 7:51