How can the mass of an invisible planet be determined?
Careful measurement and calculation has given us much knowledge about space and the universe around us. If we look at other planetary bodies of known mass that orbit near the one that is not visible, we can crunch numbers and determine the mass of the unknown. We can measure the effect the invisible body has on visible and known bodies and arrive at the numbers that account for the orbital perturbation of our known objects. And we're good at this. The idea of finding the mass of an unseen planet is the next step after "discovering" a planetary body without first seeing it by noticing a slight effect on the orbit of other planetary bodies nearby. That's how Neptune was discovered; its existence was proved by applying mathematical tools to other observations. ("Look at this data! There has to be something else out there affecting the other planets!") And that was back in 1846! Waaaay cool!
The orbital circumference of a planet is determined by both the mass and size of a planet. Although a planet will orbit the sum in an eliptical sphere shaped orbit, the circumference of these are almost always relative to the mass and density of the planet. It is also determined on how far away it is from the sun. The orbital circumference of a planet is determined by both the mass and size of a…
The mass of the Sun and the distance between the planet and Sun. As the Sun's mass is (more or less) constant, all we need to know is the distance. Technically this is called the "semi major axis" of the elliptical orbit. (If you wanted to be really, really accurate the mass of the planet does have a very very small effect.)
The force of gravity is determined by (a) the masses involved, and (b) the distance between the masses. Of course, in the case of a planet for example, you can determine the mass if you know its average density and its size. Note that for a homogeneous sphere, the force of gravity on an object outside the planet is the same as if all mass were concentrated in the center.
Planet X is a hypothetical planet once thought to exist out beyond Neptune. Astronomers discovered a discrepancy in Uranus' orbit that they thought indicated another planet beyond Neptune whose mass was affecting it. When Neptune's mass was determined using data gathered by Voyager 2, Astronomers discovered that the discrepancy was entirely due to Neptune's orbit. Since then, other trans-Neptunian objects have been discovered, but none large enough to be considered a planet.
There is a mathematical relationship between gravity and weight not mass. Mass is some thing that you always have, it doesn't change. But weight is determined by the size of the planet that they are on, bigger planets like Saturn and Jupiter get more gravity therefore making a person's weight differ