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Minimal velocity in order to revolve about an object?

  • Mass of Object 1 (M1) >>> Mass of Object 2 (M2) M1 ≈ Mass of Sun. i.e. M1 is large enough to induce gravity on objects that are relatively far away. M2 is a distance, d, away from M1. M1 exerts a gravitation "pull", vg, on M2. the velocity, vm2, of M2 is tangential to the gravitational "pull" of M1 and it stays that way for all time, t. I assume this is obvious considering the question I am asking, but just to make sure you understand. Assume all other gravitational influences are negligible. How would you find the minimal tangential velocity of M1 for it to stay in orbit around M2? There has to be a ratio between tangential velocity and gravitational pull below which you spiral inwards and crash and above which you run away. I feel as though the ratios should be set in concrete, I just don't know them. ratio between vm2 and vg. if you have equations or whatever you can express them in any fashion you wish i.e. convert everything to forces/momentums, velocities, etc. I could care less. I just want to know what the ratio is. perfect circle ratio would be cool too. Even trickier, what is the ratio between tangential velocity and distance away from M1 if M1 exerts a uniform Gravitation Field, such as inside of the event horizon of a black hole. It actually should not be that tricky. Here is the speed with which you are pulled inward: 300,000,000 m/s. So, ??? m/s Tangential vs. 300,000,000 m/s Normal required to make a perfectly circular orbit if you are 3E9 meters away? 3E12 meters? 3E15 meters? Assume the event horizon extends to a distance greater than 3E15 m. This of course is making the assumption that objects are not allowed to exceed the speed of light, which I think is wrong, but am completely incapable of proving...to explain what that means: If objects cannot exceed the speed of light, then the speed with which an object is "pulled" by gravity cannot exceed the speed of light either, so under this assumption, the Gravitational Field inside of the event horizon of a black hole would exert the same "pull" velocity towards the center of mass at all points within the event horizon. Tidal forces would differ, which is why you get crushed. but since you are supposedly incapable of exceeding the speed of light then, unlike ALL other occurrences of gravity in the universe, you would not be pulled any faster toward the center of mass at 3 meters away than you would at 3E13 meters away. which obviously makes no sense at all. But I also didn't write the rules.

  • Answer:

    Learn about centripetal acceleration and uniform circular motion. It doesn't look like you can handle the full solution to Newton's Law of Universal Gravitation, so you'll have to be satisfied with circular orbits. EDIT: Andrew, You can't even tell the difference between velocity and acceleration. Who is the idiot who passed you? Not worth writing the answer to your question.

Andrew at Yahoo! Answers Visit the source

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You seem to think that gravitational influence is a speed: "vg." And you try to talk about the "speed with which you are pulled inward" to a black hole. So you might have taken physics 1 at Georgia Tech, but I suspect you didn't do terribly well. Because the first thing they teach you is that in a gravitational field, all bodies fall at the same rate--- of ACCELERATION. > the velocity, vm2, of M2 is tangential to the gravitational "pull" of M1 and it stays that way for all time, t. I assume this is obvious considering the question I am asking, but just to make sure you understand. Actually, no, it's not obvious. Orbits come in all sorts of shapes and sizes: circular, elliptical, parabolic, hyperbolic. By specifying that the velocity must always be tangent to the pull, you're specifying that the orbit must be circular. That's leaving out a lot of possible orbits. > There has to be a ratio between tangential velocity and gravitational pull below which you spiral inwards and crash and above which you run away. Again, no. There are no "spiraling in and crashing" orbits. Not in Newtonian gravity, anyway. There are only ellipses, cirlces, parabolas, and hyperbolas, and nothing else. At any rate, for a nonrelativistic central mass, like the Earth or Sun, you can simply write down Newton's law of Universal Gravitation to find the force of gravity at a given distance d from the center: Fg=G*M1*m2/d^2. Set this equal to the centripetal force required to keep a body in a circular orbit, Fc=m2*v^2/d, and you're done. Solve for v to find the one and only UNIQUE (not minimum) speed for a circular orbit at that distance. Black holes are more complicated; you cannot use Newton's Laws, which are only approximations to GR. There are no circular orbits or stable orbits allowed at all inside the "photon sphere," long before you get to the event horizon. At that point, there are only spiral-in and spiral-out orbits. The rest of your question is basically unintelligible since you continue to insist that forces are speeds while simultaneously denigrating your pet misunderstandings of theories that you haven't bothered to study yet.

Lola F

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