Once Thomson showed that atoms consist of very light negative electrons and a much more massive positive charge, why didn’t physicists immediately consider a solar-system model of electrons orbiting a positive nucleus? Why would physicists in $1900$object to such a model?

We need to find the reason why scientist didn't consider Thomson's model of atom

At that time there was not much advancement in technology due to which for the physicists it was a tough task to imagine and study the well defined tine structure of atom.

From classical electromagnetic theory, it is assumed that when an electron revolves around the nucleus in a particular orbital it continues looses its energy and it will start to collapse inside the nucleus.

Using the concepts of Newton's third law .Physicists was in a dilemma that if inside the nucleus which type of force will hold so many protons together as because of nature of same charges they would experience a repulsive force due to coulomb's law

$F=\frac{K\times Q_1\times Q_2}{d^2}$(where Q1 and Q2 are two charges of the particles and d is the distance between them and k is the coulomb's constant) . And because of this forces a disturbance will get created in nucleus which will led it to collapse.

As Thomson also stated that a atom consists of equal number of positive and negative charges and it will cancel out the charges and net charge become zero. And because of this atom becomes neutral. But Rutherford's Gold foil experiment proves that the center of the atom contains a heavy thing . Which proves that atom is not empty.