A scientist has used mathematics to disprove popular conspiracy theories.

Dr David Grimes, of the University of Oxford, developed a formula which showed that the numbers of people involved in sophisticated conspiracies, such as fake moon landings, would have led to them being exposed.

He worked out that for something to stay a secret for over one hundred years could have involved a maximum of 125 people. However, a plot involving more than 2,521 people could stay covert no longer than five years.

Therefore, the moon landings, which took place in 1969 and involved at least 411,000 Nasa employees, could not have been faked and kept secret until now, according to the formula.

Dr Grimes said: "It is common to dismiss conspiracy theories and their proponents out of hand but I wanted to take the opposite approach, to see how these conspiracies might be possible. To do that, I looked at the vital requirement for a viable conspiracy-secrecy."

His theory is based on the notion that a certain number of people can keep a secret only for a limited amount of time. The more people involved, the less time it remains a secret.

His equation takes into account the probability of a conspiracy being accidently revealed or deliberately leaked by a whistle-blower. It was informed by evidence from real conspiracies, including Edward Snowden’s exposure of the NSA Prism project.

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Dr Grimes says that a plot to fake the moon landings would have been revealed in three years, eight months and a climate change conspiracy would have leaked in three years, nine months.

The research also scrutinised medical conspiracies. A vaccination conspiracy would have emerged in three years and two months, Dr Grimes claims, and a suppressed cancer cure would be exposed in three years and three months.

For conspiracies that do not require active maintenance, there are various factors involved in the calculation: the number of plotters, the length of time, and the effects of conspirators dying.

Dr Grimes added: "A number of conspiracy theories revolve around science. While believing the moon landings were faked may not be harmful, believing misinformation about vaccines can be fatal. However, not every belief in a conspiracy is necessarily wrong - for example, the Snowden revelations confirmed some theories about the activities of the US National Security Agency.