Yorkshire Ripper Peter Sutcliffe will tomorrow challenge a High Court judge's order that he can never be released.
Mr Justice Mitting announced his decision in London on July 16, ruling that the serial killer of 13 women must serve a "whole life" tariff.
His case will be heard tomorrow at the Court of Appeal by the Lord Chief Justice, Lord Judge, Mr Justice Calvert-Smith and Mr Justice Griffith Williams.
Now known as Peter Coonan, the former lorry driver, from Bradford, West Yorkshire, was convicted at the Old Bailey in 1981.
Sutcliffe, now 64, received 20 life terms for the murder of 13 women and the attempted murder of others in Yorkshire and Greater Manchester.
Mr Justice Mitting, when giving his ruling, said the murderer had caused "widespread and permanent harm to the living".
He said: "This was a campaign of murder which terrorised the population of a large part of Yorkshire for several years.
"The only explanation for it, on the jury's verdict, was anger, hatred and obsession.
"Apart from a terrorist outrage, it is difficult to conceive of circumstances in which one man could account for so many victims.
"Those circumstances alone make it appropriate to set a whole life term."
He said he had read statements by relatives of six murdered victims: "They are each moving accounts of the great loss and widespread and permanent harm to the living caused by six of his crimes.
"I have no doubt that they are representative of the unspoken accounts of others who have not made statements.
"None of them suggest any term other than a whole life term would be regarded by them as appropriate."
He said he had no doubt that the "appropriate minimum term is a whole life term".
Sutcliffe is being held in Broadmoor top security psychiatric hospital after being transferred from prison in 1984 suffering from paranoid schizophrenia.
It was on July 5 1975, just 11 months after his marriage, that he took a hammer and carried out his first attack on a woman.
Sutcliffe is said to have believed he was on a "mission from God" to kill prostitutes - although not all of his victims were sex workers - and was dubbed the Yorkshire Ripper because he mutilated their bodies using a hammer, a sharpened screwdriver and a knife.
Mr Justice Mitting said: "Only Rosemary West and Dennis Nilsen approach the number of victims murdered. Even they did not reach the total number of the respondent's victims."
The primary submission made on behalf of Sutcliffe was that the degree of his responsibility "was lowered by mental disorder or mental disability".
The diagnosis of psychiatrists who considered his mental condition was that he was "suffering from encapsulated paranoid schizophrenia when he committed the crimes and that his responsibility for the 13 killings was, in consequence, substantially diminished".
But the judge said: "These propositions were, however, unquestionably rejected by the jury."
He ruled: "It is not, in my opinion, open to a judge, setting a minimum term, to go behind the verdict of the jury by concluding that, although the defendant's responsibility was not proved to have been substantially diminished, he should be given the benefit of the doubt for the purpose of setting the minimum term, by concluding that it might have been."
It was the opinion of psychiatrists that Sutcliffe "suffers from a chronic treatable mental illness for which he has been willing to accept appropriate treatment, which has successfully contained it for many years".