A planet’s gravitational field surrounds the planet inside and outside reaching far out into space, but the strength become weaker the further away you get from the planet. The gravitational field is generated by the mass of the planet. The more mass it has, the stronger is its gravitational field. The table below shows some masses of objects in our solar system.

The gravitational field can't be seen directly with our eyes, but it can easily reveal itself through the effects it has on other objects: rocks fall, rain falls, and we walk safely on the surface of the Earth without fear of floating away into space. In fact, it is hard to escape from the Earth. Spaceships need huge powerful rocket engines that can generate incredible forces to lift a rocket upward while at all times gravity is pulling it back down. If the rockets fail or shut off too soon, then gravity pulls the rocket back down to crash on the surface of the Earth; however, if the rocket engines burn long enough, they can lift the rocket far enough away from the Earth that gravity is so weak that it is now easy for the spacecraft to escape into space. Moons orbiting planets would fall like rocks if they didn’t have enough orbital speed to keep them revolving around a planet. Thus a study of the behavior of a moon reveals much about the gravitational force of a planet.

In order for the teams to determine the mass of a planet, they first had to learn a few things about the moons of the planet. The moons of the planet orbit because of the planet’s gravity. If the planet had no gravity, then a moon would rush away into space because of its orbital speed. The planet exerts a force on the moon which pulls it inward toward the planet – gravity always pulls things inward, it never pushes things away. If the force due to gravity is not strong enough, then the moon would spiral away from the planet eventually escaping out into interplanetary space. If the force of gravity is too strong, then the moon would spiral inward and crash on the planet. If the force is in between these extremes, then the moon would stay in a perpetual orbit around the planet.

So the teams had to know the period of revolution of the moons and the distance each moon is away from the new planet. Well, they had already determined these properties. Thus using several of Sir Isaac Newton's physics equations plus the definition of circles, 

The teams were able to determine the mass of the new planet as being 4.7 x 10²² kg  or 127 times less than Earth but 3 times more than Pluto.