Flux, Luminosity, Distance, Size

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The discussion revolves around calculating the distance to galaxy Cluster B based on its observed brightness compared to Cluster A, concluding that Cluster B is 200 Mpc away. The relationship between apparent size and distance indicates that objects farther away appear smaller, but the exact formula for this relationship is unclear to the participants. Additionally, the conversation touches on the implications of gravitational interactions between galaxies at a redshift of 0.8, specifically regarding their current separation. Participants seek guidance on how to approach these calculations and clarify the relationships involved. Overall, the thread emphasizes the complexities of astronomical measurements and the need for further assistance in understanding these concepts.
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1) You observed two galaxy clusters. You have determined the distance to Cluster A (by Cephied variables) to be 50 Mpc. You find the galaxies in Cluster B to be on average 16 times fainter than those in Cluster A. How far away is Cluster B? How does the (apparent) average size of galaxies in Cluster B compared to that of Cluster A?
[Using the formula flux=luminosity/(4*pi*d^2), I have that the answer to the first part is 200 Mpc, but I don't know how to do the second part (in red), can someone please help me?]


2) The scale factor of the universe R(t) is equal to 1 (by definition) at the current epoch. This question compares the universe at a redshift of 0.8 to today.
If 2 galaxies were in each other's gravitational potential, and orbiting each other with an orbital of 0.5 Mpc at z=0.8. Assuming the orbit is stable, how far apart are they today?
[can someone give me some hints? I really have no clue how to calculate this...]

Thanks a lot!:smile:
 
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If the object is farther, the object's apparent size should be smaller...but what is the exact relationship?
 
Can anyone please help me?
 
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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