The judge will consider all the facts, but contempt is an open ended sentence and the judge decides how long you stay in jail.
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Although contempt is an open ended sentence, the Court will most likely hold what is called a status hearing in a few months to determine if the Defendant should be placed on what is called work release. At that point the Defendant could be released in the morning to find or maintain a job and then he would report back to the jail at night until such time as he pruged himself of contempt by paying that one months worth of child support. A judge will not leave a Defendant in jail forever as our Georgia Supreme Court has held, we do not operate debtors prisons.
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Your question is how long? Until the judge decides to let him out. To minimize this time, it is important that you work with a local, comeptent, experienced attorney to discuss the case, and the best plan going forward. For starters, the reasons for non-appearance listed in this posting are going to be a difficult story to sell the court. In three days, the court is going to figure there was some way he could have contacted them.
Anyway, an attorney can help you with this.