Quote:
Originally Posted by lemit
I am trying to make self-evident that my talent lies in language. It doesn't lie in math. Could you explain what the formulae mean, or at least what they might mean to one of David Letterman's dumb guys?
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No trouble, mate. But, I should say with assuredness: math is a language and not knowing it certainly doesn’t put into question your intelligence. I don’t know German. I would hope that says little of my competence. I would suspect you are unfamiliar with math, and that is all.
If you situate yourself some distance away from a mass like the earth and you throw something away from that mass... I suppose you might think of a person in a rocket sitting stationary above earth’s atmosphere shooting a cannonball away from the earth—there is a certain velocity for that cannonball beyond which it will not fall back toward the earth nor could it find an orbit around the earth. If the cannonball is shot away from the earth with a speed greater than the earth’s escape velocity then it will just keep moving away from the earth forever. It won’t be gravitationally bound to the earth.
So, turn the situation around a little. Let’s say you are wandering about in your rocket in space not far from earth with your good buddy Walter Cruttenden. You come across a cannonball which you notice is moving away from the earth. Your buddy Walter says “I bet that cannonball is orbiting the earth. I bet the earth and the cannonball make up a binary system”.
So, you indulge your friend and measure the velocity of the cannonball relative to the earth with your high-tech onboard radar tracking sensors (why not... it’s a nice rocket). You find that it is moving 200 kilometers per second away from the earth. But, earth’s escape velocity where you are is only 11 km/s. This means anything in that particular area of space going faster than 11 km/s away from earth will not achieve an orbit around the planet, but will rather just keep going away from it forever. That would pretty-well rule out the possibility that the cannonball is orbiting the earth. It’s going too fast.
But, here is where I throw in a curveball, what if the earth were more massive? You and Walter in the rocket might pretend that earth is twice as massive as you think it is. If that were the case then the escape velocity in that area of space would be greater than 11 kilometers per second. The next logical question would be: “how massive would the earth need to be for this cannonball to be gravitationally bound to the earth?”. The cannonball is moving 200 km/s and if the earth were massive-enough it could pull the cannonball back toward it and perhaps the cannonball could achieve an orbit. So, the question at hand is: what mass does the earth need to be in order to be bound to this cannonball?
That is the question that my first post answers. The cannonball is the sun. We know that the sun is moving away from Sirius at 7,600 meters per second (direct observation tells us this) and we know the distance to Sirius so we can find the mass that Sirius would need to be in order for the sun to be bound to it. The answer is that Sirius would need to be 17,748 times as massive as our sun. If it is any less massive than that then the sun is exceeding the escape velocity necessary to break free of Sirius’ gravity forever. In actual fact, Sirius A and Sirius B combined are only 3 times as massive as the sun. This makes it completely impossible for us to be in orbit with that star. It almost needs to be as massive as a supermassive black hole to catch us at this distance and speed. Not possible.
My second post is similar, but deals with the tangent (or sideways) velocity. If you move fast-enough past a mass then it will not catch you and put you in orbit (think of a meteor almost grazing the earth as it flies by). We are moving fast enough in a tangent direction past Sirius that we cannot be in a binary orbit with it (given that it has a reasonable mass)
That ok?
~modest
