Friedmann equations treated a case where there is uniformly distributed matter and cosmological constant. This is a good approximation on a large enough scale. However, in any given galaxy or solar system you don't have uniformly distributed matter: you have clumps of matter (stars, planets) and near-vacuum in between. So some other solution of the field equation applies.
A study of the Schwarzschild and de Sitter-Schwarzschild solutions gives some good general guidance on what to expect within any given solar system. By employing Birkhoff's theorem one learns that for the case of a single spherical star at the middle of a spherical void inside a spherically symmetric matter distribution, the solution in the void (the region outside the star, and inside the rest) is Schwarzschild (or de Sitter-Schwarzschild) even if the further matter is expanding outwards. So this helps you to see why gravitationally bound systems do not expand, to first approximation, with the cosmic expansion. A planet orbiting such a star will have an orbit whose radius and period does not change with time.
Since in fact there is never perfect spherical symmetry nor perfect vacuum, the precise situation will not be quite like that, but it gives the correct starting-point for further calculation.
