Thank you very much for this session.
Regarding the 4000 m comet that crashed into Jupiter. 4000m, 4km, 2.5 miles is a lot. I am happy Jupiter took that blow. Jupiter is a huge planet, according to
http://www.universetoday.com/15149/size-of-jupiter/ said:
The planet’s diameter is 11.2 times larger than Earth’s. Jupiter’s volume is 1321 times larger than Earth’s and it’s surface area is 122 times that of Earth’s.
If the Earth got hit by a comparatively similar sized body, what would the diameter be? Below there are some considerations which do involve math, but I have tried to reduce it.
To compare one needs to take the difference of size into consideration. If Jupiter is so much bigger than Earth, we would have an idea, if we found the volume of a spherical body that was 1321 times smaller than the comet with the size of 4000m that hit Jupiter.
The formular for the volume V of a sphere with the radius r is:
V=(4/3)*pi*(r^3)
In the formular we notice that (4/3)*pi is a constant. What makes the difference in volume is therefore the size of the radius.
Since (r^3) means r*r*r if the radius of another comet is half of the radius of 4000 meter ball, we would have 1/8th of the volume of the original body, if one third of the radius then the volume would be 1/27, if it had been a quarter then 1/64 and so on. If the radius of the body had been 1/10 of the original its volume would be a 1000 times smaller.
For our purpose a 1000 times smaller is not enough, we need to find a body that is 1321 times smaller. As it turns out, if the radius is 1/11 of the original we would get af volume which is 1331 times smaller and this is close enough for our puposes. Since the diameter is two times the radius, if the radius has to be about 11 times smaller, so does the diameter.
This means that if a 4000 meter comet hits Jupiter an equivalent punch would be an Earth hitting comet with a diameter of 4000m/11 which is a staggering 360 meters. [One could get to the number 11 in other ways, like arguing that since the diamter of Jupiter is 11.2 times the diameter of Earth, therefore the Jupiter sized Comet would need to have a diameter that is 11 times smaller if it was to hit Earth.]
There is only one "small" problem, Jupiter is a gas planet! Although the volume is 1321 times more than that of the Earth, the mass is only 318 times more. This means the mean density on Earth is (1321/318) or 4.15 times higher. Therefore we need a comet that contains more mass than the 360 meters ball, we already have. If the radius of the comet had been 50% more, we would have a body with a mass that is (1.5)^3 =3.4 times more. That is not enough, we increase to 60% more and this gives us (1.6)^3 which is about 4.1 more mass and since we needed 4.15, this ansver is sufficient.
This means that if the cross section size of our 360 meter comet is increased by 60% or if you like multiplied by 1.6 then we have a comet body which would be comparatively equivalent to what hit Jupiter the other day. The shocking part is that this gives us a comet with a diameter of 580 meters!
One might say that this is not fair, since Jupiter is a gas planet, it absorbs the comet much better than a solid Earth, therefore if fairness was to prevail the comet for the Earth should be smaller.
In any case next time it is reported an object of a given size has hit Jupiter, we can divide the diameter by 11 and multiply the result by 1,6 to get the size that would fit the Earth.
Below is a list of estimates regarding the frequency of bigger objects colliding with the Earth, even though this presuppoes they are random and equally distributed.
Kinetic energy at Crater diameter Frequency (years)
Impactor atmospheric
diameter entry impact
100 m (330 ft) 47 Mt 3.8 Mt 1.2 km (0.75 mi) 5,200
130 m (430 ft) 103 Mt 31.4 Mt 2 km (1.2 mi) 11,000
150 m (490 ft) 159 Mt 71.5 Mt 2.4 km (1.5 mi) 16,000
200 m (660 ft) 376 Mt 261 Mt 3 km (1.9 mi) 36,000
250 m (820 ft) 734 Mt 598 Mt 3.8 km (2.4 mi) 59,000
300 m (980 ft) 1270 Mt 1110 Mt 4.6 km (2.9 mi) 73,000
400 m (1,300 ft) 3010 Mt 2800 Mt 6 km (3.7 mi) 100,000
700 m (2,300 ft) 16100 Mt 15700 Mt 10 km (6.2 mi) 190,000
1,000 m (3,300 ft) 47000 Mt 46300 Mt 13.6 km (8.5 mi) 440,000
Apparently a 580 meter object does not come in often. If a change in diameter from 400 -700 meter changes the frequency from 100,000 to 190,000 years, then it roughly means that 500 meter object might come every 130,000 years, and a 600 meter object every 160.000 years, but again that is statistics.
Apart from the size, it is very important to know the energy it carries, which includes the kinetic as well as the electric charge. The electric charge and its influence is hard to evaluate, but the size and speed one can simulate.
On this page one can play with the options for different sizes of impact, ajusting for speed, density, impact angle and so on. They also say:
http://impact.ese.ic.ac.uk/ImpactEffects/ said:
[...]The minimum impact velocity on Earth is 11 km/s. Typical impact velocities are 17 km/s for asteroids and 51 km/s for comets. The maximum Earth impact velocity for objects orbiting the sun is 72 km/s.
[...]
The impact angle is measured from a plane tangent to the impact surface. This angle is 90 degrees for a vertical impact. The most probable angle of impact is 45 degrees.[...]
If a 580 meter comet hit the Earth at 45 degrees with a speed of 51 km/s, and we were within a 1000 km of the impact, we would most likely hear the sound from the impact some 50 minutes later, but it would not make the Earth shake much at that distance. However there are also people who will be closer, and for them it will be a very traumatic experience, if they even survive.
There are some quesitons besides the physical impact calculations: Would the Earth environment be significantly affected by a highly charged object, or is the cosmic environment affected? What happens to Jupiter when it takes in a 4000 m object. What happens to Earth when Jupiter is hit by a comet?
