Scientists use different models to study the mass of a star, but their results do not converge. Perhaps difficulties arise due to the fact that a space object does not fall into the field of view of many telescopes.
People have been watching the Pole Star, also known as Polaris, for centuries. It is Earth's closest Cepheid, a type of star that pulsates regularly. Polaris is also part of a binary system, it has a fainter sister known as Polaris B. It would seem that the North Star has long been studied. But in fact, no one still can determine its mass and distance to the Earth.
Astrophysicists have several ways to calculate the mass, age, and distance of a star like Polaris. One of them is the stellar evolution model. Researchers study the brightness, color and pulsation rate of a star and use this data to figure out how large and bright it is, and at what stage of life it is. There are other ways to study Polaris, but their results are not consistent with models of stellar evolution.
Researchers have not yet studied the orbit of Polaris B well enough, but they have enough data to apply Newton's law of gravity to measure the mass of two stars. These measurements indicate that Polaris is about 3.45 times the mass of the Sun. This is much less than the mass that is obtained using the stellar evolution model. It defines the mass of Polaris as about seven times the mass of the Sun.
This star system is strange in other respects as well. Age calculations for Polaris B show that the star is much older than its bright sister, which is unusual for a binary system. Typically, two stars are roughly the same age. Scientists have created a huge set of Polaris models to see if these models can agree on all the data, but they have failed.
The problem may be that Polaris is located above the North Pole of the Earth, that is, out of the field of view of most telescopes. And telescopes, equipped with the necessary equipment to measure the properties of a star, are usually designed to study much fainter and more distant stars.