How is momentum conserved in which two satellites connect

If we have:
m₁ as the mass of the first satellite
m₂ as the mass of the second satellite
v₁ as the velocity of the first satellite before the connection
v₂ as the velocity of the second satellite before the connection
v₁' as the velocity of the first satellite after the connection
v₂' as the velocity of the second satellite after the connection

The momentum is conserved following this equation:
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

If the collision is perfectly elastic or the two satellites connect perfectly and move with a single velocity:
m₁v₁ + m₂v₂ = (m₁ + m₂)v'
where v' is the velocity of the two connected satellites