For a plot to last five years, it would need to involve just 2,521 people

Moon landings would have been exposed in three years and eight months

He then formulated how likely it would be that the secrets would be kept

From the moon landings being an elaborate hoax, to climate change deniers, there are many conspiracy theories that are believed by a large number of people worldwide.

But the amount of people who would have been involved in keeping such large-scale secrets suggests that if they were true, they would have been exposed by someone by now.

With this in mind, a physicist has calculated how many people would have potentially worked on some of the most popular theories, and what is the likelihood of them all keeping a secret.

A physicist from Oxford University calculated how many people would have potentially worked on some of the most popular theories, and what is the likelihood of them all keeping them a secret. Using this model, the truth about the moon landings (pictured) being a hoax would have been exposed in three years and eight months

Using this model, the truth about the moon landings being a hoax would have been exposed in three years and eight months.

A climate change fraud would have been uncovered in three years nine months, a vaccination conspiracy would take three years and two months to be revealed, and a suppressed cancer cure would come to light after three years and three months.

The formula was created by Dr David Robert Grimes from Oxford University.

He initially created an equation to express the probability of a conspiracy being either deliberately uncovered by a whistle-blower, or inadvertently revealed by a bungler.

This factored in the number of conspirators, the length of time, and even the effects of conspirators dying, whether of old age or more nefarious means.

Dr Grimes looked at four alleged, popular conspiracy theories, estimating the maximum number of people required to be in on each 'secret'. For example, he calculated that 411,000 people would have feasibly needed to be involved in, or have knowledge of, the moon landings being a hoax (landing pictured)

Moon landing reveal is pictured top left. A climate change fraud would have been uncovered in three years nine months (top right), a vaccination conspiracy would take three years and two months to be revealed (bottom left), and a suppressed cancer cure would come to light after three years three months (bottom right)

However, the equation required a realistic estimation of the chances of any one individual revealing the truth.

To put this to the test, he used the revelations made about the NSA Prism project by Edward Snowden and its timescale, as a base.

Dr Grimes then looked at four alleged, popular conspiracy theories, estimating the maximum number of people required to be in on each 'secret'.

For example, he calculated that 411,000 people would have feasibly needed to be involved in, or have knowledge of, the moon landings being a hoax.

THE FOUR CONSPIRACY THEORIES STUDIED Nasa moon-landing conspiracy: The successful 1969 Apollo 11 mission first put men on the moon, a seminal achievement in human history. Yet even since that day, there has been a persistent fringe belief group that strongly believe the moon landings were faked, mocked up for propaganda purposes. In 2013 it was estimated 7 per cent of Americans subscribe to this view. Those advocating this conspiracy claim there are inconsistencies in pictures taken on the moon’s surface, despite these claims being comprehensively debunked. Climate change conspiracy: Climate-change denial has a deep political dimension. The belief that a cure for cancer is being withheld by vested interests is a long-standing one. Stock image Despite the overwhelming strength of evidence supporting the scientific consensus of anthropogenic global warming, there are many who reject this consensus. Of these, many claim that climate-change is a hoax staged by scientists and environmentalists, ostensibly to yield research income. Vaccination conspiracy: Conspiratorial beliefs about vaccination are endemic in the anti-vaccination movement. It is estimated that roughly 20 per cent of Americans hold the long de-bunked notion that there is a link between autism and the MMR vaccine, a belief which has reduced uptake of important vaccinations in several countries. Anti-vaccination beliefs and scare-mongering are also endemic in the internet age, with vaccine critical websites asserting dubious information. Cancer cure conspiracy: The belief that a cure for cancer is being withheld by vested interests is a long-standing one. It is often used as a universal deus ex machina for those pushing an alternative alleged cure, and assertion of the conspiracy theory functions as an explanatory device to explain the complete paucity of clinical evidence for such claims. Such claims can be detrimental to patients, some of whom abandon conventional treatment for the lofty but ill-founded promises of alternative medicine. Source: Dr David Grimes/Plos One Advertisement

A total of 405,000 people would know about climate change being a fraud, 22,000 people would be covering up that vaccinations are unsafe, and 736,000 people would know about a cancer cure being suppressed.

These figures came from analysing the number of people involved in organisations related to the hoax, such as Nasa, the White House administration, pharmaceutical companies and climate change groups.

In each case, the number of conspirators and the time before the conspiracy was revealed were over-estimated to ensure that the odds of a leak happening were a 'best case scenario' for the conspirators.

From this he determined that all of the four plots would have been revealed long before now, and all within four years.

These figures came from analysing the number of people involved in organisations related to the hoax, such as Nasa (a graphic produced by the agency showing rising global temperatures is pictured), the White House administration, pharmaceutical companies and climate change groups

If the conspiracy theories were true, a total of 405,000 people would know about climate change being a fraud, 22,000 people would be covering up that vaccinations (stock image) are unsafe, and 736,000 people would know about a cancer cure being suppressed

He then looked at the maximum number of people who could take part in an intrigue in order to keep it a secret for any substantial length of time.

For a plot to last five years, the maximum was 2,521 people.

To keep a scheme operating undetected for more than a decade, fewer than 1,000 people can be involved.

A century-long deception should ideally include fewer than 125 collaborators.

Dr Grimes then looked at the maximum number of people who could take part in an intrigue in order to keep it a secret. For a plot to last five years, the maximum was 2,521 people. To keep a scheme operating undetected for more than a decade, fewer than 1,000 people can be involved (pictured in the chart above)

Even a straightforward cover-up of a single event, requiring no more complex machinations than everyone keeping their mouth shut, is likely to be blown if more than 650 people are accomplices.

'Not everyone who believes in a conspiracy is unreasonable or unthinking. I hope that by showing how eye-wateringly unlikely some alleged conspiracies are, some people will reconsider their anti-science beliefs,' Dr Grimes explained.

'This will of course not convince everyone; there's ample evidence that belief in conspiracy is often ideological rather than rational, and that conspiracy theories thrive in an echo chamber.

'This makes challenging the more odious narratives much more difficult. If we are to address the multitudinous difficulties facing us as a species, from climate change to geo-politics, then we need to embrace reality over ideologically motivated fictions.

'To this end, we need to better understand how and why some ideas are entrenched and persistent among certain groups despite the evidence, and how we might counteract this.'