Side effects
GAS-RELATED EFFECTS
A) Late orchestra.
Considering the propagation speed of sound in the gases considered, if spectators who live in Pluto were invited to listen to the concert, they should be warned that the performance could begin with the proverbial fifteen academic years late.
Wanting to shorten the waiting times, it would be necessary to increase the speed of sound propagation in the gas and consequently increase the temperature of the gas.
To reach the maximum speed of sound (equal to 36100 meters per second, in accordance with theoretical research carried out by Queen Mary University, Cambridge University, the Institute for High Pressure Physics in Troitsk, and Tohoku University in Sendai), and therefore have a travel time of the semimajor axis equal to t=ssemimajor axis vprop. sound, gas=7.3810123.61104=6.5 years, a temperature equal to:
Helium case:
tv max, He=M0v2R=4.003(3.61104)220,812,58,314=3.7108K
Hydrogen case:
tv max, H2=M0v2R=2.016(3.61104)228.720.48.314=4.46108K
Instead, if a spectator on Pluto wanted to see the orchestra playing in "real" time with a powerful telescope, it would be enough to wait for a time equal to (in the case of hydrogen):
t=safelio, Plutonec=7.3810123.0108=24600 s=6 hours and 50 minutes
NB It should be noted that in reality the speed of light in materials is different from that in a vacuum, consequently the formula to be used would be (considered vlight, H2=10r0r): safelium, Pluto10r0r=safelium, Pluto0r0r (with 0 dielectric constant of vacuum, r relative dielectric constant, 0 magnetic permeability of vacuum r relative magnetic permeability)
B) Friction.
One of the main problems related to the idea of "immersing" the solar system in a large quantity of gas is the presence of friction: the resistance that these gases would have on the motion of the planets would have disastrous consequences to say the least; the planets have a revolution speed of the order of magnitude of hundreds of thousands of km/h, the presence of gases would slow down their progress, consequently the kinetic energy would be transformed into heat. This is the same effect present in atmospheric reentry and as in it the planets would reach very high temperatures (the designers of heat shields use an approximate rule for which the peak temperature in degrees k that an object reaches in atmospheric reentry is equal to the speed in m/s). Furthermore, this deceleration would ensure that, in the space of time necessary, the planets stop completely or rather their speed decreases to zero. Since the planets (and the other bodies of the solar system) are "falling" towards the Sun, a fall which remains in equilibrium thanks to the constant speed at which the planets move again, once the speed reaches 0, they would go to crash and burn inside the Sun.
Slowing down of the motions of revolution
Friction can be calculated with the following formula:
Fr=mgV 2VL2
Where
v is the speed of revolution of the planet (for the Earth 29780.5556 m/s),
V L the speed limit,
m its mass
g is the acceleration due to gravity to which it is subjected by the Sun.
Two intermediate steps are required to solve this formula.
Find g:
g=Gmsr2
With→
G, universal gravitational constant= 6.67430x10 -11 (N m 2 / kg)
m= 1.98892×10 30 kg
r= 1.4833 × 10^11m
We have therefore
g=G 1.98892×1030 (1.4833 ×1011) 20.00603344 m/s2
Then it is necessary to calculate the limiting speed, i.e. the maximum speed that a body falling into a fluid can reach:
VL=mg6RT
With→ , viscosity of the fluid, in the case of hydrogen, at a temperature of -240°=
3,5x10 -5 poises
RT = 6373044.737 m
m= 5.97219 x 10 24 kg
A further intermediate step is needed for the resolution of this formula to obtain the viscosity of hydrogen at a temperature of -180°. The following formula can be used, where TB is the boiling point of hydrogen
(-252.9°) and µG1 the viscosity of the fluid at temperature T1
µG2 = µG1 .[(T2/T1) 3/2 (T1+1.47.TB)]/[T2+1.47.TB)]→
3.5x10 -5 [(-180/-240) 3/2 (-240+1.47(-252.9)]/[-180+1.47(-252.9)]= 2.52x10 - 5 poises
We then calculate the speed limit:
VLH2=(5.97219 1024)0.006033446(2.52 10-5) 6373044.737= 1.190282321 x 10 19 m/s
Finally, it is now possible to calculate the deceleration to which the Earth would be subjected if immersed in hydrogen:
Fr, H2=(5.97219 1024)0.00603344(29780.5556) 2(1.1902823211019)2= -2.25561118610 -7 m/s 2
It should be noted that the negative sign placed in front of the result is of purely physical derivation, as the friction has a direction opposite to the speed.
To calculate the temperature that the Earth would reach, for example, at the end of the concert, lasting about 57 m (3420s) we use the circular motion formulas:
TKVfVf=( t)+Vi (-2,25561118610-73420)+29780,5556= 29780,55483K° = 29507,40483 C°
Melted orchestra????
This is more than 5 times the surface temperature of the Sun (5504.85 C°). At this temperature no material, not even diamond (with a melting point of around 4000 C°) can resist, the buildings would melt and collapse on an equally liquid asphalt within seconds of the start of the exhibition, our atmosphere would vanish and we humans and other life forms would not end up pleasantly.
It can be seen how in the previous calculation an almost identical final and initial speed is obtained, this is because the deceleration is too small for there to be a significant variation in such a short time but, despite being so small, the Earth would still come to crash into the Sun in span of this time:
t=Vf-Vi0-29780.5556-2.2556118510-7=1.320287247 1011s
4187 years
The calculations and results in this section refer to the only hypothetical case of what would happen to the Earth immersed in hydrogen. For results relating to the other planets in both gases that are assumed to be used in this project, the link for the google spreadsheet with the missing data is attached:
HOW LONG WILL THE PLANETS STOP, AND HOW LONG WILL THEY BURN? (There may be some discrepancy between the data in the spreadsheet and the data on this document, as the spreadsheet tends to approximate results differently than we used for our calculations).