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