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The force on a planet is given by Newton’s universal law of gravitation ($F = -G.(m_1.m_2)/r^2$)

The force on an electron circling the nucleus is given by $F = 1/(4pi epsilon_0)(q_1.q_2)/r^2$

They are similar, both varying inversely with distance squared, but not identical - it is mass that causes gravitational attraction, and charge that causes electrostatic attraction.

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