kepler's third law
I’m told that the Sun weighs 2,000 million million million million tons. That if course, sounds very heavy, and I suppose it could be fairly accurate. Nevertheless, for me these questions arise. How do they know the weight of the Sun? Who was it that somehow managed to go out there and weight the Sun? And where did they get a scale big enough to set the Sun on to get this very accurate sounding weight? Ok, I’m being sarcastic, but then again, these are legitimate questions. I’m told that there is a formula they use to figure the mass of a planet.
First one has to calculate the mass of the Sun. There are apparently several ways to do so. One way is to use Kepler’s third law: “M = 4r³?²/T²G, where r is the distance between the Earth and the Sun, T is the time it takes for the Earth to orbit the Sun, and G is the gravitational constant. The mass of the Sun is about 2×10³? kg.” Another way is to use the mass formula: “Mass = Density x Volume. The mass of the Sun’s core is estimated to be 3.0 x 10³¹ kg, and the mass of the outer shell is estimated to be 1.1 x 10³¹ kg.” The third way is to “divide the total mass by 1.98855 times 10 to the 30th power.” From what I can see, the common methos is the Kepler’s third law. Once you have that figured, you are ready for the next step…the weight of the Sun.
That process is as complicated as, or nearly as complicated as the methods to figure the mass of the Sun. Apparently, it all has to do with the mass of the Sun, the mass of the Earth, the gravitational pull on the Earth by the Sun, and the distance between the two squared. Or more scientifically written, “The gravitational attraction between the Earth and the sun is G times the sun’s mass times the Earth’s mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun.” If that makes perfect sense to you, then you are 
likely a better scientist or mathematician than the average person. So even if I could fully understand that process, and I don’t, I still have to ask one question, where is the proof that its true and accurate. I realize that there is no way to definitively prove the weight of the Sun, the Earth, or any other planet, and maybe this is somehow he most accurate guess possible. I don’t know, but maybe they should say that the Sun weighs approximately 2,000 million million million million tons. At least, that would stop such silly questions from people like me.
