>>797467
>Why does Orthodoxy accept 3 marriages
The sacraments are not magic. Their effect on us depends of our disposition to them.
The sacrament of marriage unites a man and a woman to become two consubstantial hypostases, in the image of the Trinity. But the couple only grows in that direction if they are recepetive to the sacrament and have faith.
What happens if they move in the opposite direction? They commit a grave sin - they destroy the marriage, they blaspheme the sacrament. What then happens? Either the Church preserves a legal fiction, therefore permitting them to blaspheme the sacrament further, with the hope that they are reconciled to one another soon, or the Church takes away the sacrament, that is, permits a divorce, which is an offense, as we are not to tear apart what the Lord has bound together. Both are cases of economy, and it is up to the spiritual father of the couple to figure out what is best, and it is up to the bishop to give permission or not to this or that use of economy.
Remarriage is only allowed if a party got the short end of the stick, so to say. If a husband or wife was abused or cheated on by their partner, and this is what led to the divorce, should they be therefore condemned to celibacy for life when the sin was not their will to begin with? What if they have children who need two parents, too? In this case the Church may permit a remarriage, a second try at it, even though the first one ended catastrophically.
A third marriage is extremely rare, in fact service books usually don't have the service for it.
Note also that remarriage comes with a penance of not taking communion for a while, that is, excommunication.
Remember, finally, that unlike in Catholicism where the sacrament is given by the husband and wife to one another with the priest or deacon blessing the union in the name of the Church, in Orthodoxy the sacrament is given by the Church. In Catholicism, nothing can take back the sacrament, except the death of a spouse, and the sacrament can be invalidated if the two parties didn't have the right intent when it was given. But in Orthodoxy, the Church can take back the sacrament it gave, and for it to be invalidated it would take something very extreme and unusual (such as the priest who gave the sacrament not actually having been a priest at the time the sacrament was given).
>and birth control
Birth control is not permitted. In recent years, a less rigorist approach has been introduced, according to which non-abortifacient birth control may be allowed, by economy, for a couple for which having a child right now would be very spiritually damaging and dangerous, and abstinence is too difficult for the people involved or is simply not possible for one reason or another.
We basically don't condemn birth control as being a sin equivalent to murder, so in very specific cases it might be permitted as a temporary solution. Abortifacient contraceptives are equivalent to murder, or more simply the same as murder, however.
I forgot where the canons on divorce and remarriage are, and I'm busy now. I might look into it later.
Also, Catholics on this board seem to compare permitting contraception by economy to Arianism, or at least to ordaining female priests. Your priorities are not right. Permitting divorce may be more properly compared to permitting female priests, as it is a difference in the understanding of a sacrament, at least. But whether X is a sin is rather low in the list of priorities one should have, compared to theological issues about who Jesus is, or what the sacraments mean.