Monday, August 25, 2014

Two Moons: Mars our Second Moon

There's a message going around on Whatsapp and Facebook that goes something like this
"On 27th August 2014 there will be two moon. The whole world is waiting for it. On this day Mars will be very bright and like moon everyone can see it with naked eyes. This day it will be 34.65 M Miles away from Earth. On this day do not forget to see this at 12.30 night. Because you will see two moons in the sky. This event will happen again in the year 2287"
This is wrong. This whole thing is a rumor. This won't happen for the reasons I state below

The first problem is the distance quoted:
First lets concentrate on "Mars will be 34.65 M Miles away from earth", now that's equivalent to saying its 55.44 M km away from earth. Now if you do the calculations correctly you'll find that the closest mars can ever get is approximately 54,557,514 km. That's a difference of 110,000 km.

Fig 1: Earth Mars position
The above figure shows the position of Earth and Mars on 27th August, 2014. If you observe the figure, it shows the actual Earth Mars position, I've circled Earth with red and Mars with yellow. The green double headed arrow line shows approximately the position at which Mars can get closest to the Earth. Since the planets are going counterclockwise Earth has already passed that point. Even if it was at that point it will pass it by the time Mars reaches the other end of the line.
(Image snapshot of the Solar System model at the website Solar System Scope)

In short the fact that is stated is incorrect, but even if we assume this fact as correct it still won't be enough. In fact lets be safe and assume the mars is just 50 million km away from us.

Second problem is the brightness:
The second problem is "On this day Mars will be very bright and like moon" now I'm not sure how they defining brightness. I'm assuming by brightness they mean the amount of light coming from mars and the moon will be about the same. Sure mars is quite larger than our moon But it's even more further, so not only does less light reach Mars from the Sun but the reflected light has to travel a long way back to earth, and this reflected light will spread even more. So there wouldn't be much light coming from it in any case.

What about the size of the planet. Size is just an illusion to begin with. The apparent size is in scientific term called angular spread, but there's a very easy way to calculate the size, it's just a simple division.
Fig 2: Equation for angular size

If this calculation for two different object gives almost the same number they will appear to be of the same size. Take the Sun and the Moon for example, their angular size is Coincidentally almost the same (approx 0.009). And this is the reason why the moon exactly covers the sun during total solar eclipse.

Fig 3: Diamond Ring
Incidentally if you are reading a book and if you're holding it around 30 cm from you the size of the letter 'o' in book is the same as that of the moon or sun as a result if you were to look at the sun and fit it between your finger like you're holding it. the moon would fit in the same distance between your finger and so will the letter 'o' in the books. In other words if you look at the size of the letter 'o' on your book that's the size of the sun in the sky.

Coming back, the diameter of Mars is approx 6800km, just a little over the radius of the Earth. At its closest point we are assuming it would be 50 M km. If you use these numbers you should come to a result, the angular size of Mars which would be 0.0001 (I assumed that we would be doing observation from the surface of the Earth) which is around 90 times less than the Moon or Sun even when we assumed a distance closer than it could possibly achieve and it is still not be as visible as the moon.

All in all you would never ever observe 2 Moons ever, to be more safer you'd not observe it on 27th August, 2014.