Binary-star system, gravity + centripetal force question?

AI Thread Summary
In a binary-star system with each star having a mass of 1.36e30 kg and a distance of 1.1e8 km between them, the gravitational force equals the centripetal force for their revolution around the center of mass. The user initially struggled with the calculations, particularly with the conversion of kilometers to meters and the correct application of the formulas. After some confusion regarding the values for radius and diameter, the user realized the mistake was simply in unit conversion. Once corrected, the calculations became straightforward. This highlights the importance of accurate unit conversion in astrophysical calculations.
basenne
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1. In a certain binary-star system, each star has the a mass of 1.36e30 kg, and they revolve about their center of mass. The distance between them is 1.1e8 km. What is their period of revolution in Earth years?
2.
gravity = centripetal force
(g*m*m)/d^2 = (mv^2)/r
3. I've tried plugging in numbers, tried 1/2 of 1.1e8 for R and 1.1e8 for D(diameter), didn't work. Not quite sure what I'm doing wrong. I know that v^2 becomes (diameter/time)^2 and to solve from there, however, I'm just not sure where to start. (
 
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Nevermind, got it. It's actually really easy, I just forgot to change kilometers into meters... fail!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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