The planet known as PH3c nearly avoided detection because it has a highly inconsistent orbit time around its Sun, due to the gravitational influence of other planets in its system.
"On Earth, these effects are very small, only on the scale of one second or so," said Joseph Schmitt, a Yale University graduate student and first author of the paper.
"PH3c's orbital period changed by 10.5 hours in just 10 orbits," said Schmitt.
That inconsistency kept it from being picked up by automated computer algorithms that search stellar light curves and identify regular dips caused by objects passing in front of stars.
Researchers discovered the new planet with the help of Planet Hunters programme coordinated by Yale University and University of Oxford.
"It harnesses the human dimension of science," said Debra Fischer, who leads the exoplanets group at Yale and is a co-author of the paper.
"Computers can't find the unexpected, but people can, when they eyeball the data," Fischer said.
The discovery also enabled astronomers to better characterise two other planets - one on each side of PH3c.
An outer planet, PH3d, is slightly larger and heavier than Saturn, for example. An inner planet, PH3b, may have a rocky composition, like Earth.
"Finding the middle planet was key to confirming the others and allowing us to find their masses," Schmitt said.
"The outer planet's orbital period also changes slightly, by about 10 minutes. You need to see both planets' changing orbital periods in order to find out the masses of the planets. One planet doesn't give enough information," said Schmitt.
There's also a quirky aspect of the planetary trio, Schmitt added. The outer planet's year is 1.91 times longer than the middle planet's year, and the middle planet's year is 1.91 times longer than the inner planet's year.
"We're not sure if this is just a coincidence or whether this might tell us something about how the planets were formed," Schmitt said.
The finding was published in The Astrophysical Journal.