In 1897, J. J. Thomson announced his discovery of the electron and the fact that atoms must therefore have some structure. At the time not all scientists were convinced that atoms even existed, but Einstein's 1905 explanation of Brownian motion provided convincing evidence that atoms were real.
Thomson's model of atomic structure is often called the plum pudding model. He postulated that the negatively charged electrons, he had recently discovered, were scattered throughout a cloud of positive charge, like the plums in plum pudding.
The plum pudding model could not however predict why atoms absorbed and emitted spectral lines. The real deathblow to the plum pudding model came from experiments showing that atoms have nuclei.
In 1909 Ernest Rutherford, one of Thomson's students, conducted the first nuclear scattering experiments. Rutherford and his students scattered alpha particles, now known to be helium nuclei, off the atoms in a sheet of gold foil. Rutherford's scattering experiments showed that atoms consist of a positively charged nucleus surrounded by negatively charged electrons.
Rutherford therefore envisioned the electrons orbiting the nucleus in a matter analogous to the planets orbiting the Sun. The electrical forces between protons and electrons follow Coulomb's law, which has the same mathematical form as Newton's law of gravity. Hence negatively charged electrons orbiting a positively charged nucleus in a manner analogous to the solar system is a very reasonable idea.
Despite Rutherford's indisputable evidence for a very small atomic nucleus, physicists of the time had problems with the solar system analogy of atomic structure.
The density of the nucleus would have to be unimaginably high. It in fact is.
The positively charged nucleus should fly apart because of the electromagnetic repulsive forces between positive charges, whereas in the plum pudding model the negative charges mixed in with the positive charges could hold the atom together. Physicist later discovered two types of nuclear forces: strong and weak. The strong nuclear force overwhelms the electromagnetic force within atomic nuclei and holds the nuclei together.
There were however two much more serious problems with Rutherford's solar system analogy of atomic structure.
These problems were finally resolved by Niels Bohr and the Bohr model of the hydrogen atom.
Knight, R.D., Physics for Scientists and Engineers with Modern Physics, Pearson, 2004.
Heisenberg Uncertainty Principle