Closed Kepler orbits are ellipses with the Sun at one focus.
The force felt by the planet points in the direction of the Sun. As such, it is not a central force, since the focus is not the center.
I am confused. The force should be central. What is my misunderstanding?
Answer
We generally choose to use the location of the sun as our origin. You're correct in identifying this is at the focus of the ellipse. We then choose to take quantities relative to the Sun as origin. e.g. the radial distance for an ellipse from a focus is given by $$ r=\frac{a(1-e^2)}{1\pm e\cos\theta}, $$ whereas to give the distance from the center of the ellipse, the expression is $$ r=\frac{ab}{\sqrt{b^2\cos^2\theta + a^2\sin^2\theta}}. $$
Further we define things like $\vec{r}$ from the Sun, and angular momentum $\vec{r}\times\vec{p}.$ Now I'll try to explain why we choose to do this.
Consider if we were to use the center of the ellipse instead. This position of the center depends upon the orbital elements of the orbit we're looking at. So the center of our origin for the Earth-Sun, would be different to that of Sun-Jupiter. That sounds incredibly fiddly to work with. E.g. the angular momentum for Jupiter would be meaningless to compare to the angular momentum of Earth, since it's taken about a different point. If instead we use the Sun, then the origin stays put, and the two angular momenta become meaningful to compare.
Further it has good physical meaning, since as you also correctly identify, it's where gravity is pulling us towards. This means we get to easily utilize the spherical symmetry, if we choose that origin.
So to conclude, the focus as origin is physically meaningful. The location of the center of the ellipse is something that depends on the particular orbit you're looking at, and not a very useful origin to do the mathematics with. Then when we say something is central, we mean around our chosen origin, which here is the focus.
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