Originally posted by wolfgang59
There must have been some estimation of the size of the orbit surely?
I'm thinking those three numbers can lead to a solution but they did not mention the size of the orbit, radius or diameter. I think a solution would relate the orbital period to the escape velocity of Alcor A. In any orbital the escape velocity is 1.414 (sqr root of 2) times the orbital velocity, but not sure how to apply that in this case. If the orbit is say, at 16 billion Km (ten billion miles) you get one answer but if it is at 1.6 billion Km you get another. I think we can relate it to our suns' orbitals, since the mass of the sun is half that of Alcor, it should be easy to equate what a 90 year orbit would be in our solar system and then double the mass and recompute for Alcor. Seems kind of cheating though.
I just did a bit of google and found the orbital period of Uranus is 84.1 years, close to Alcor's newly found companion. I guess I could work it out from there.
So Uranus orbits at 6729.3 meters/sec, escape velocity of Uranus from Sol is 1.414 times that or 9515.3 meters/second. The sun is about 2E30 Kg. That's a start anyway.
One Wiki piece says the orbital period is 84.323326 years or 30,799.095 days which works out to 2,661,041,808 seconds. Uranus maxes out at 3 E9 Km and mins at 2.7 E9 Km, so I used a # halfway between to get a halfasssed assessment of the average distance, used 2.85 E9 Km as distance. Sort of making an attempt at simplifying to a circular orbit.
The formula for orbital velocity is V=(GM/r)^0.5 G=grav. constant, M=mass, r=radius. So solving for R, = GM/V^2. So The mass of the dwarf doesn't matter, just the mass of the primary. Seems a bit of a conundrum, if I knew the radius I could figure the velocity, if I don't know the radius, I don't know the velocity.