Can ISON hit the Earth? WARNING math inside

I am not an astronomer but have basic knowledge of Newton physics. My goal here is to estimate how much energy we need in order to change the course of Ison so it will hit the Earth.

So let's start.

t: it takes 28 days for ISON to reach the Earth from Sun (2.4 x 10e6 sec)

Se: closest approach to the Earth 63,000,000 km (6.3 x 10e10 m)

Ss: distance from Earth to Sun: 149,600,000 km (1.5 x 10e11 m)

Vi: speed of Ison 86000 m/s = 8.6 x 10e4 m/s

m: estimated mass 7,000,000,000 kg (7 x 10e12 g) to 7,000,000,000,000 kg (7 x 10e16 g) from [link to www.nasa.gov] , for our calculation we take lower number.

angle between Earth - Sun - Projected Ison path
atan(Se/Ss) = atan(6.3 x 10e10 / 1.5 x 10e11) = atan(0.2625) = 14.7 degrees

This is how much the course of Ison or one of its debrees must be changed in order to hit the Earth.

The speed we need to push Ison in perpendicular vector towards the Earth
V = Se/T = 6.3 x 10e10 / 2.4 x 10e11 = 2.6 x 10e4 = 26000 m/s

This is how much energy needed to do that:
E = mVxV/2 = 7 x 10e12 x 6.76 x 10e8 / 2 = 2.4 x 10e21 Joels

(1 kiloton of TNT equals to 5 x 10e12 Joels so we need
2.4 x 10e21 / 5 x 10e12 of kilotons = 4.8 x 10e8 kilotons = 30,000,000 Hiroshima bombs)

It looks a lot but considering total Kinetic energy of Ison:

8.6x8.6x 10e8 x 7 x 10e12 / 2 = 259 x 10e20 = 2.6 x 10e22 Joels = 5.2 x 10e9 kilotons = 325,000,000 Hiroshima bombs

we need only 9% of the total Ison energy to be redirected in order to change the course towards the Earth.
It does not look a lot.

Let's take only small chunk of Ison (we don't need the full comet for the disaster. For example for one Million of Hiroshima bomb we need 1/325 of Ison's mass thus it is enough to redirect 9%/325 = 0.028% of the total Ison energy to change the course of this chunk.
Remember we used lowest mass estimation. So the number can be even less.

Astromut and other experts!
Am I wrong? If yes show where.

Last Edited by Sergman on 12/01/2013 05:58 PM