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I'm just looking to gain a basic intuitive understanding of the forces at work in tidal stripping and their direction/motivation etc. I'm struggling to grasp the underlying principles and it is making any questions/further understanding very tricky.

From my lecture notes I have the expression:

$$\frac{d^2 \bf{r'}}{dt^2} = - \nabla\phi_s(\bf{r'}) - \nabla\phi_G(\bf{r'}) + \nabla\phi_G(\bf{0})$$

This is accompanied by the description:

Consider a satellite star located at $\textbf{r} = \textbf{r}' + \textbf{R}_G$, where $\textbf{R}_G$ is the satellite barycentre in the host galaxy frame. To calculate the tidal force acting on this particular star we subtract the acceleration of the satellite’s centre of mass by the host galaxy to the relative acceleration of a member star at the position $\textbf{r}'$ where $\phi_s$ and $\phi_G$ are the gravitational potentials of the satellite and the host galaxy, respectively.

So my understanding from this is that a given star at point $\textbf{r}'$ in relation to the satellite barycentre/centre of mass point will have both gravitational potentials acting in tandem and the acceleration will be provided with the delta of these fields relative to this position $\textbf{r}'$. Further to this, is an additive term that arises from the galactic host's gravitational field at the origin? I think my confusion arises from the final term, I do not see where it comes from or what it really represents.

Cheers in advance.

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