The Star by Herbert Wells

In January (about 1900, presumably), the people of Earth awaken to the notion that a strange luminous object has erupted, into the Solar System, after disturbing the normal orbit of the planet Neptune. Indeed, such object is a luminous celestial body, whose luminosity is distinguishable on the sky about the constellation of Leo.
Although initially it is only of interest to astronomers, eventually the world media announces that it is a whole star, heading in a collision course toward the center of our star system. The star has already consumed Neptune. Many people are concerned by this, but on the whole it amounts to little more than a temporary fad.