Inverse square law

Three of the AP sheet's headline results share this shape. Gravitation gives $|\vec{F}_g| = Gm_1m_2/r^2$, Coulomb's law gives $|\vec{F}_E| = k|q_1q_2|/r^2$ with $k = 9.0 \times 10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$, and the field of a point charge gives $|\vec{E}| = k|q|/r^2$. Recognising the pattern means one piece of reasoning covers all of them.

The reasoning is a factor of change. Multiply $r$ by $n$ and the quantity divides by $n^2$: three times as far apart is one ninth the force. Science practice 2.D asks for exactly this, predicting factors of change from functional dependence, so a great many questions want the ratio and no numbers at all.

Two things to keep straight.

First, $r$ is measured between centres, not between surfaces. A satellite $600\ \text{km}$ above the ground is not at $r = 600\ \text{km}$; add Earth's radius.

Second, potential energy is not an inverse square law. The sheet prints $U_G = -Gm_1m_2/r$ and $U_E = kq_1q_2/r$, both with a single power of $r$. Force falls as $1/r^2$ while the associated energy falls as $1/r$, and a question that doubles a separation is often checking that you know which is which.