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 mass of the planet, the mass of the sun and the distance between the two.
No. A planet's gravitational pull is determined by the planet's mass. A planet's orbital speed is determined by the the mass of the Sun and the planet's distance from the Sun.
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 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 escape velocity is determined by the gravity of the planet which in turn is determined by the mass and size of the planet
True.
Yes.
No. Weight is the measure of how much force a planet pulls an object, that force is determined by the planet's mass and radius, and each planet has a different mass and radius.
Volume
All planets have gravity, and will attract other objects. The strength of the attraction is determined by the mass of the planet and the distance to the object.
Mass and volume are not determined by density. Rather density is determined by mass and volume
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.)
No, the mass of a planet does not equal the size of that particular planet.