Despite persistent rumors to the contrary it is never possible for Mars to appear as large as the full Moon in the sky.
There is a persistent urban legend that Mars will appear as large in the sky as the full Moon. This myth often takes the form of forwarded Emails, and specifies a date when Mars will be so large. The date passes; Mars stays the same size. Like any urban legend, the myth resurfaces with a new date and some altered details. Astronomers, including the one writing this article, are inundated with questions about the veracity of rumors that Mars will appear as large as the full Moon.
It is physically impossible for Mars to ever appear as large as the full Moon in the sky.
If you get an Email making such a claim, do not believe it and do not forward it to all your friends.
The Moon has a diameter of about 3500 km compared to about 6800 km for Mars. Mars is therefore almost twice as large as the Moon in terms of its actual physical size.
So why can't it appear as large as the Moon in the sky? The key is their distances.
A car on a highway will appear larger as it drives closer and then appear smaller as it drives away, even though the actual size of the car is not changing. Similarly a distant large truck can appear smaller than a nearby compact car.
Despite being only half the actual size, the Moon will always appear larger than Mars in the sky because it is so much closer. The Moon is 384 thousand kilometers from Earth. Earth is an average distance of 150 million kilometers from the Sun and Mars averages 228 million kilometers from the Sun. Hence, when Mars is at its closest approach to Earth, called opposition, it will be about 78 million kilometers from Earth. This distance can vary by about 10% or so for different oppositions of Mars because the orbits are not perfectly circular.
At its closest approach, Mars is roughly 200 times as far away as the Moon, yet it is only about twice as large. Hence at its closest approach Mars appears about 1/100 the size of the full Moon. Repeat.
It is physically impossible for Mars to ever appear as large as the full Moon in the sky.
For similar reasons, Mars also can never be as bright as the full Moon in the sky.
In August 2003, the opposition of Mars occurred when Mars was at its closest distance to the Sun. Therefore it was the closest opposition in about 60,000 years. Mars appeared, on that date, larger and brighter than normal, but it was still tens of millions of kilometers from Earth. So it was still no where close to the size and brightness of the full Moon in the sky.
It is possible to magnify the image of Mars in a telescope to the point where the magnified image of Mars is as large as the unmagnified image of the full Moon. But it is also possible to magnify the image of a microbe so that it appears larger than an elephant.
In order for Mars to appear as large as the full Moon in the sky a catastrophic event would have to rip the planets from orbits that have been stable for about 5 billion years. It ain't gonna happen!