Re: Creationism, Myth and Catastrophism
Posted: Wed Jan 08, 2025 7:13 pm
337545
SUN'S CAPTURE OF SATURN SYSTEM
ESCAPE/CAPTURE VELOCITIES
Jupiter has an average orbital speed of ~13.07 km/s; Saturn's Speed is ~9.69 km/s.
Perplexity.AI did the following work for me, though it seems likely incorrect to some extent.
To calculate the required speeds for a rogue planet to be captured by a one solar mass star at various distances (including 1 AU, 5 AU, 10 AU, 20 AU, 30 AU, 50 AU, and 100 AU), we will use the escape velocity formula.
The escape velocity v_e is given by: v,e=(2GM/r)^1/2
Where:
G=6.674×10^−11 m3/kg,s^2
M=1.989×10^30 kg
r is the distance from the star in meters.
Summary of Required Speeds for Capture
Distance (AU); Required Speed for Capture (km/s)
1: ~617.7 (Earth's distance)
5: ~276.5 (Jupiter's distance)
10: ~195.5 (Saturn's distance)
20: ~138.8
30: ~113 (Pluto's distance)
50: ~82.6
100: ~58.3
GAS CLOUD DENSITY
To determine how dense gas and dust would need to be at 10 AU to slow a rogue planet enough for capture, we must consider several factors, including the planet's initial speed, the drag force exerted by the gas and dust, and the time over which this deceleration occurs.
Key Considerations
1. Initial Speed of the Rogue Planet:
The speed of a rogue planet approaching a solar mass star at 10 AU can be significant. For example, if it were traveling at speeds around 195.5 km/s (as previously calculated for escape velocity at this distance), it would need to be slowed considerably to enter a stable orbit.
2. Drag Force:
The drag force 'Fd' acting on the rogue planet due to gas and dust can be approximated using the equation:
F_d=1/2C_dρAv^2
where:
C_d is the drag coefficient (typically around 1 for spherical objects),
ρ is the density of the gas/dust,
A is the cross-sectional area of the planet,
v is the velocity of the planet.
3. Deceleration:
The deceleration 'a' experienced by the planet can be calculated using Newton's second law:
F=ma ⟹ a=F_d/m
where 'm' is the mass of the rogue planet.
4. Density Calculation:
To find out how dense the gas and dust need to be, we can rearrange our equations to solve for ρ:
ρ=2F_d/C_dAv^2
Conclusion
The density of gas and dust at 10 AU would need to be approximately 0.93 kg/m³ or denser in order to slow down a rogue planet traveling at around 195.5 km/s sufficiently for capture into orbit around a solar mass star. This density is comparable to that of Earth's atmosphere at sea level (which is about 1.225 kg/m³), indicating that substantial amounts of gas and dust would be required in that region of space for effective deceleration and capture.
DECELERATION TIME & DISTANCE
To estimate how long it would take for a rogue planet to be captured by a star at 10 AU, we need to consider the deceleration process due to the drag from gas and dust, as well as the distance the planet must travel during this capture phase.
Key Factors for Capture Time and Distance
1. Initial Speed: As previously discussed, let's assume the rogue planet is initially traveling at approximately 195.5 km/s.
2. Deceleration: If we assume that the drag force from gas and dust can provide sufficient deceleration, we previously calculated that a density of about 0.93 kg/m³ would be needed to achieve an average deceleration of about 10 m/s².
3. Time to Slow Down: To find out how long it would take for the rogue planet to slow down enough for capture, we can use the formula:
t=(vi−vf)/a
where:
vi is the initial velocity (195,500 m/s),
vf is the final velocity (let's assume it needs to drop to around 97,750 m/s for capture),
a is the deceleration (10 m/s²).
Summary
Time to Capture: Approximately 2.72 hours.
{ERROR} Distance Traveled During Capture: Approximately 1,435.7 km.
This calculation assumes constant deceleration due to drag from gas and dust at a density sufficient to slow the planet effectively. The actual dynamics could be more complex due to variations in density and other factors in a real astrophysical environment.
ELECTRICAL REPULSION
If both a rogue planet and a gas cloud have the same electric charge and high amperage, this could indeed affect the deceleration of the planet. Here’s how:
Electric Charge Interaction
1. Electromagnetic Forces: Charged objects exert electromagnetic forces on each other. If the rogue planet and the gas cloud have the same charge, they would repel each other due to Coulomb's law, which states that like charges repel. This repulsion could potentially counteract some of the deceleration effects caused by drag from the gas cloud.
2. Increased Drag: If the gas cloud is also charged, it may create an electric field that interacts with the charged surface of the rogue planet. Depending on the configuration and relative motion, this interaction might enhance the drag force experienced by the planet, leading to increased deceleration. For example, if the gas particles are able to ionize or become polarized in response to the electric field of the planet, this could create additional forces that contribute to slowing down the planet.
3. Radiation Effects: Accelerating charged particles emit radiation (bremsstrahlung), which can result in energy loss. If high amperage is involved, and if particles within the gas cloud are also accelerating due to interactions with the charged planet, they may radiate energy as well. This could lead to a complex interplay where both the planet and gas cloud lose energy through radiation.
Summary of Effects on Deceleration
Repulsion: If both have like charges, they will repel each other, which may reduce effective deceleration from drag.
Enhanced Drag: If conditions allow for additional electromagnetic interactions (e.g., ionization), this could increase drag and thus enhance deceleration.
Energy Loss: The presence of high amperage and accelerating charges could lead to significant energy loss through radiation, affecting overall dynamics.
Conclusion
In conclusion, while having like charges would generally lead to repulsion between the rogue planet and gas cloud, under certain conditions, it could also enhance deceleration through electromagnetic interactions. The net effect would depend on various factors such as charge density, relative velocities, and environmental conditions within the gas cloud.
JUPITER-SIZE PLANET CAPTURE
To calculate how long it would take for a Jupiter-sized planet (with Jupiter's density) to be slowed sufficiently for capture in a gas cloud, we need to consider several factors, including the planet's mass, the drag force exerted by the gas cloud, and the desired deceleration.
Key Parameters
1. Mass of Jupiter:
Jupiter's mass is approximately 1.898×10^27 kg.
2. Density of Jupiter:
The average density of Jupiter is about 1.326 g/cm^3, which is equivalent to 1326 kg/m^3.
3. Cross-Sectional Area:
Assuming Jupiter has a radius of about 71,398 km (or 7.1398×10^7 m), the cross-sectional area A can be calculated as:
A=πr^2=π(7.1398×10^7)^2≈1.597×10^16 m^2
4. Initial Speed:
Let's assume the rogue planet is initially traveling at a speed of about 195.5 km/s=195500 m/s.
5. Desired Final Speed for Capture:
For capture, we might aim to slow it down to about half its initial speed (around 97.75 km/s=97750 m/s).
6. Drag Force Calculation:
The drag force F_d acting on the planet due to the gas cloud can be calculated using:
F_d=1/2(C_dρAv^2)
where:
C_d is the drag coefficient (assumed to be around 1),
ρ is the density of the gas in the cloud (let's assume a typical value for a dense molecular cloud of about 100 kg/m3),
v is the speed of the planet.
Calculation Steps
1. Calculate Drag Force:
Using an assumed density of gas (100 kg/m3):
F_d=1/2(1)(100)(1.597×10^16)(195500)^2
This results in:
F_d=0.5∗100∗1.597×10^16∗(3.82×10^10)
F_d=0.5∗100∗1.597×10^16∗3.82×10^10≈3.05×10^36 N
2. Calculate Deceleration:
Using Newton’s second law:
a=F_d/m
where m=1.898×1027 kg
a=3.05×10361.898×10^27≈1.605×10^9 m/s^2
3. Time to Slow Down:
Using the formula for time based on initial and final speeds:
t=vi−vfa
Substituting values:
t=(195500 m/s−97750 m/s)/(1.605×10^9 m/s^2)
t=(97750 m/s)/(1.605×10^9 m/s^2)≈6.09×10−5 s
Distance Traveled During Deceleration
Using the distance formula under constant deceleration:
d=v_it+1/2at^2
Substituting in our values:
d=(195500)(6.09×10^−5)+0.5(−1.605×10^9)(6.09×10^−5)^2
Calculating this gives:
First term: d_1=11.91 m
Second term: Calculate using acceleration and time squared.
Summary
Given these calculations:
Time to Slow Down for Capture: Approximately very short time due to high deceleration.
Distance Traveled During Deceleration: A very small distance due to rapid deceleration.
Conclusion
In reality, these calculations suggest that while theoretically possible to slow down such a massive object quickly in a dense gas cloud, practical scenarios would involve complex interactions and varying conditions that could significantly alter these results. The assumptions made regarding drag coefficients and gas densities would need to be validated against real astrophysical data for more accurate modeling.
CORRECTED? TIME DURATION OF CAPTURE
Since it calculated that the time to slow down is just a fraction of a second and the distance traveled during deceleration is under 12 meters, that would suggest the planet hit a brick wall in outer space. So I asked AI to review its calculations to look for errors.
It then corrected its deceleration calculation, which changed the duration of deceleration to ~1.55 hours, which seems possibly reasonable. But the distance traveled, ~1354 km., during the deceleration is obviously way off. So I said: If the planet were initially moving at nearly 200 km/s as you say, and slowed down to just below 100 km/sec in 1.55 hours, it would have traveled between 558,000 km and 1,116,000 km {in that time}. So your estimate of 1354 km is way wrong. It replied.
CORRECTED? DISTANCE OF CAPTURE
Thank you for your patience and for pointing out the discrepancy. You're correct that if a rogue planet is initially moving at nearly 200 km/s and slows down to just below 100 km/s over a period of 1.55 hours, the distance traveled would indeed be much greater than the previously calculated 1354 km. Let's re-evaluate the calculations to ensure accuracy regarding the time, distance, and deceleration.
Summary of Corrected Results
Time to Slow Down for Capture: Approximately 1.55 hours.
Distance Traveled During Deceleration: Approximately 817,125 km, which aligns with your observation about the expected distance based on speed and time.
Conclusion
The previous estimate of 1354 km was incorrect due to an error in calculating the distance traveled during deceleration. Thank you for your correction; it highlights the importance of careful calculations in astrophysical scenarios.
{I'm skipping some of the calculations and showing only the new distance calculation.}
Distance Calculation
Using the average speed:
d=v_avg × t
Now substituting in the values:
1. Convert time from seconds to hours: {It should have said from hours to seconds}
1.55 hours is equivalent to:
t=1.55×3600≈5580 s
2. Calculate Distance:
Using the average speed:
d=v_avg × t=146625 m/s × 5580 s
Calculating this gives:
d≈817,125,000 m ≈ 817,125 km
That would be a little under 6 Jupiter diameters. That would be for a thick gas cloud about as dense as Earth's atmosphere. So I asked for a calculation for less dense gas clouds.
CAPTURE TIME & DISTANCE FOR THINNER GAS CLOUDS
To determine the deceleration time and distance for a Jupiter-sized planet moving through a gas cloud with a density that is 10% of the previously assumed value, we will follow a similar approach as before, adjusting the calculations based on the new density.
{I'm skipping the calculations.}
Summary of Results with Adjusted Density
Time to Slow Down for Capture: Approximately 16.9 hours.
Distance Traveled During Deceleration: Approximately 8,922 km.
The time seems plausible, but the distance is way wrong again. I explained the error like I did earlier, but it came up with 8,917 km, almost the same as before. So I said: Dope. Can't you see you keep coming up with the wrong distance that's way too short? Find the average speed between the initial velocity and the final velocity and multiply that by the time to get the distance. I found that its error was converting meters to kilometers properly. Finally, it did it correctly, I assume, as follows.
I apologize for the repeated errors in my previous responses. Thank you for your patience. Here’s the corrected summary with the accurate distance stated clearly:
Summary of Results with Adjusted Density
Time to Slow Down for Capture: Approximately 16.9 hours.
Distance Traveled During Deceleration: Approximately 8,917,000,000 meters, or 8,917,000 kilometers.
CAPTURE TIME & DISTANCE IN MUCH THINNER GAS CLOUD
Those answers look a bit plausible. But then I switched to Copilot, since Perplexity stopped answering. I said: If a Jupiter-size rogue planet traveling at 200 km/s encountered a stationary gas cloud 1% as dense as Earth's atmosphere, how long a time and distance would it take to reduce to 100 km/s?
Calculating this involves a lot of physics. Here’s a simplified approach:
1. Mass of Jupiter: 1.898×10^27kg
2. Initial Velocity: 200 km/s
3. Final Velocity: 100 km/s
4. Density of Gas Cloud: 1% of Earth's atmosphere (1.225 kg/m^3) = 0.01225 kg/m^3
Using the concept of drag force, assuming the planet loses velocity primarily due to the drag force from the gas cloud:
The drag force is given by:
F_d=1/2(ρv^2C_dA)
where:
ρ = density of the gas cloud
v = velocity of the planet
C_d = drag coefficient (let's assume C_d = 2.2 for a rough sphere)
A = cross-sectional area of Jupiter
The cross-sectional area A is:
A=πr^2
… The loss in kinetic energy (ΔKE) will be equal to the work done by the drag force:
ΔKE=W=F_d⋅d
… d≈6.59 billion kilometers
… t≈1.38 years
6,590,000,000km/778,500,000km ≈ 8.47 times around Jupiter's orbit. Jupiter now takes almost 12 years to orbit once, so in 8.5 orbits, it would take over 100 years. So it needs to slow down a lot more to reach its present orbital speed. I then asked Copilot to calculate for a ten times greater density gas cloud, to compare with Perplexity. After calculation it said this.
If the gas cloud density were ten times greater, it would take approximately 50.8 days and 659 million kilometers for the rogue planet to reduce its speed from 200 km/s to 100 km/s.
So that would be a little under one Jupiter orbit, i.e. about 85% of one orbit. I don't imagine a gas cloud 10% of Earth's atmosphere density was likely, but if it remained in place for a few years, Jupiter could have slowed to its present speed in a few years. Same applies to Saturn. Electric charges on the cloud and the planet could have helped a lot too.
Perplexity said 17 hours, 9 million km to reduce speed in ~10% Earth's atmosphere density for the gas cloud.
Copilot said 51 days, 660 million km. I'm guessing Copilot has the better estimate.
SUN'S CAPTURE OF SATURN SYSTEM
ESCAPE/CAPTURE VELOCITIES
Jupiter has an average orbital speed of ~13.07 km/s; Saturn's Speed is ~9.69 km/s.
Perplexity.AI did the following work for me, though it seems likely incorrect to some extent.
To calculate the required speeds for a rogue planet to be captured by a one solar mass star at various distances (including 1 AU, 5 AU, 10 AU, 20 AU, 30 AU, 50 AU, and 100 AU), we will use the escape velocity formula.
The escape velocity v_e is given by: v,e=(2GM/r)^1/2
Where:
G=6.674×10^−11 m3/kg,s^2
M=1.989×10^30 kg
r is the distance from the star in meters.
Summary of Required Speeds for Capture
Distance (AU); Required Speed for Capture (km/s)
1: ~617.7 (Earth's distance)
5: ~276.5 (Jupiter's distance)
10: ~195.5 (Saturn's distance)
20: ~138.8
30: ~113 (Pluto's distance)
50: ~82.6
100: ~58.3
GAS CLOUD DENSITY
To determine how dense gas and dust would need to be at 10 AU to slow a rogue planet enough for capture, we must consider several factors, including the planet's initial speed, the drag force exerted by the gas and dust, and the time over which this deceleration occurs.
Key Considerations
1. Initial Speed of the Rogue Planet:
The speed of a rogue planet approaching a solar mass star at 10 AU can be significant. For example, if it were traveling at speeds around 195.5 km/s (as previously calculated for escape velocity at this distance), it would need to be slowed considerably to enter a stable orbit.
2. Drag Force:
The drag force 'Fd' acting on the rogue planet due to gas and dust can be approximated using the equation:
F_d=1/2C_dρAv^2
where:
C_d is the drag coefficient (typically around 1 for spherical objects),
ρ is the density of the gas/dust,
A is the cross-sectional area of the planet,
v is the velocity of the planet.
3. Deceleration:
The deceleration 'a' experienced by the planet can be calculated using Newton's second law:
F=ma ⟹ a=F_d/m
where 'm' is the mass of the rogue planet.
4. Density Calculation:
To find out how dense the gas and dust need to be, we can rearrange our equations to solve for ρ:
ρ=2F_d/C_dAv^2
Conclusion
The density of gas and dust at 10 AU would need to be approximately 0.93 kg/m³ or denser in order to slow down a rogue planet traveling at around 195.5 km/s sufficiently for capture into orbit around a solar mass star. This density is comparable to that of Earth's atmosphere at sea level (which is about 1.225 kg/m³), indicating that substantial amounts of gas and dust would be required in that region of space for effective deceleration and capture.
DECELERATION TIME & DISTANCE
To estimate how long it would take for a rogue planet to be captured by a star at 10 AU, we need to consider the deceleration process due to the drag from gas and dust, as well as the distance the planet must travel during this capture phase.
Key Factors for Capture Time and Distance
1. Initial Speed: As previously discussed, let's assume the rogue planet is initially traveling at approximately 195.5 km/s.
2. Deceleration: If we assume that the drag force from gas and dust can provide sufficient deceleration, we previously calculated that a density of about 0.93 kg/m³ would be needed to achieve an average deceleration of about 10 m/s².
3. Time to Slow Down: To find out how long it would take for the rogue planet to slow down enough for capture, we can use the formula:
t=(vi−vf)/a
where:
vi is the initial velocity (195,500 m/s),
vf is the final velocity (let's assume it needs to drop to around 97,750 m/s for capture),
a is the deceleration (10 m/s²).
Summary
Time to Capture: Approximately 2.72 hours.
{ERROR} Distance Traveled During Capture: Approximately 1,435.7 km.
This calculation assumes constant deceleration due to drag from gas and dust at a density sufficient to slow the planet effectively. The actual dynamics could be more complex due to variations in density and other factors in a real astrophysical environment.
ELECTRICAL REPULSION
If both a rogue planet and a gas cloud have the same electric charge and high amperage, this could indeed affect the deceleration of the planet. Here’s how:
Electric Charge Interaction
1. Electromagnetic Forces: Charged objects exert electromagnetic forces on each other. If the rogue planet and the gas cloud have the same charge, they would repel each other due to Coulomb's law, which states that like charges repel. This repulsion could potentially counteract some of the deceleration effects caused by drag from the gas cloud.
2. Increased Drag: If the gas cloud is also charged, it may create an electric field that interacts with the charged surface of the rogue planet. Depending on the configuration and relative motion, this interaction might enhance the drag force experienced by the planet, leading to increased deceleration. For example, if the gas particles are able to ionize or become polarized in response to the electric field of the planet, this could create additional forces that contribute to slowing down the planet.
3. Radiation Effects: Accelerating charged particles emit radiation (bremsstrahlung), which can result in energy loss. If high amperage is involved, and if particles within the gas cloud are also accelerating due to interactions with the charged planet, they may radiate energy as well. This could lead to a complex interplay where both the planet and gas cloud lose energy through radiation.
Summary of Effects on Deceleration
Repulsion: If both have like charges, they will repel each other, which may reduce effective deceleration from drag.
Enhanced Drag: If conditions allow for additional electromagnetic interactions (e.g., ionization), this could increase drag and thus enhance deceleration.
Energy Loss: The presence of high amperage and accelerating charges could lead to significant energy loss through radiation, affecting overall dynamics.
Conclusion
In conclusion, while having like charges would generally lead to repulsion between the rogue planet and gas cloud, under certain conditions, it could also enhance deceleration through electromagnetic interactions. The net effect would depend on various factors such as charge density, relative velocities, and environmental conditions within the gas cloud.
JUPITER-SIZE PLANET CAPTURE
To calculate how long it would take for a Jupiter-sized planet (with Jupiter's density) to be slowed sufficiently for capture in a gas cloud, we need to consider several factors, including the planet's mass, the drag force exerted by the gas cloud, and the desired deceleration.
Key Parameters
1. Mass of Jupiter:
Jupiter's mass is approximately 1.898×10^27 kg.
2. Density of Jupiter:
The average density of Jupiter is about 1.326 g/cm^3, which is equivalent to 1326 kg/m^3.
3. Cross-Sectional Area:
Assuming Jupiter has a radius of about 71,398 km (or 7.1398×10^7 m), the cross-sectional area A can be calculated as:
A=πr^2=π(7.1398×10^7)^2≈1.597×10^16 m^2
4. Initial Speed:
Let's assume the rogue planet is initially traveling at a speed of about 195.5 km/s=195500 m/s.
5. Desired Final Speed for Capture:
For capture, we might aim to slow it down to about half its initial speed (around 97.75 km/s=97750 m/s).
6. Drag Force Calculation:
The drag force F_d acting on the planet due to the gas cloud can be calculated using:
F_d=1/2(C_dρAv^2)
where:
C_d is the drag coefficient (assumed to be around 1),
ρ is the density of the gas in the cloud (let's assume a typical value for a dense molecular cloud of about 100 kg/m3),
v is the speed of the planet.
Calculation Steps
1. Calculate Drag Force:
Using an assumed density of gas (100 kg/m3):
F_d=1/2(1)(100)(1.597×10^16)(195500)^2
This results in:
F_d=0.5∗100∗1.597×10^16∗(3.82×10^10)
F_d=0.5∗100∗1.597×10^16∗3.82×10^10≈3.05×10^36 N
2. Calculate Deceleration:
Using Newton’s second law:
a=F_d/m
where m=1.898×1027 kg
a=3.05×10361.898×10^27≈1.605×10^9 m/s^2
3. Time to Slow Down:
Using the formula for time based on initial and final speeds:
t=vi−vfa
Substituting values:
t=(195500 m/s−97750 m/s)/(1.605×10^9 m/s^2)
t=(97750 m/s)/(1.605×10^9 m/s^2)≈6.09×10−5 s
Distance Traveled During Deceleration
Using the distance formula under constant deceleration:
d=v_it+1/2at^2
Substituting in our values:
d=(195500)(6.09×10^−5)+0.5(−1.605×10^9)(6.09×10^−5)^2
Calculating this gives:
First term: d_1=11.91 m
Second term: Calculate using acceleration and time squared.
Summary
Given these calculations:
Time to Slow Down for Capture: Approximately very short time due to high deceleration.
Distance Traveled During Deceleration: A very small distance due to rapid deceleration.
Conclusion
In reality, these calculations suggest that while theoretically possible to slow down such a massive object quickly in a dense gas cloud, practical scenarios would involve complex interactions and varying conditions that could significantly alter these results. The assumptions made regarding drag coefficients and gas densities would need to be validated against real astrophysical data for more accurate modeling.
CORRECTED? TIME DURATION OF CAPTURE
Since it calculated that the time to slow down is just a fraction of a second and the distance traveled during deceleration is under 12 meters, that would suggest the planet hit a brick wall in outer space. So I asked AI to review its calculations to look for errors.
It then corrected its deceleration calculation, which changed the duration of deceleration to ~1.55 hours, which seems possibly reasonable. But the distance traveled, ~1354 km., during the deceleration is obviously way off. So I said: If the planet were initially moving at nearly 200 km/s as you say, and slowed down to just below 100 km/sec in 1.55 hours, it would have traveled between 558,000 km and 1,116,000 km {in that time}. So your estimate of 1354 km is way wrong. It replied.
CORRECTED? DISTANCE OF CAPTURE
Thank you for your patience and for pointing out the discrepancy. You're correct that if a rogue planet is initially moving at nearly 200 km/s and slows down to just below 100 km/s over a period of 1.55 hours, the distance traveled would indeed be much greater than the previously calculated 1354 km. Let's re-evaluate the calculations to ensure accuracy regarding the time, distance, and deceleration.
Summary of Corrected Results
Time to Slow Down for Capture: Approximately 1.55 hours.
Distance Traveled During Deceleration: Approximately 817,125 km, which aligns with your observation about the expected distance based on speed and time.
Conclusion
The previous estimate of 1354 km was incorrect due to an error in calculating the distance traveled during deceleration. Thank you for your correction; it highlights the importance of careful calculations in astrophysical scenarios.
{I'm skipping some of the calculations and showing only the new distance calculation.}
Distance Calculation
Using the average speed:
d=v_avg × t
Now substituting in the values:
1. Convert time from seconds to hours: {It should have said from hours to seconds}
1.55 hours is equivalent to:
t=1.55×3600≈5580 s
2. Calculate Distance:
Using the average speed:
d=v_avg × t=146625 m/s × 5580 s
Calculating this gives:
d≈817,125,000 m ≈ 817,125 km
That would be a little under 6 Jupiter diameters. That would be for a thick gas cloud about as dense as Earth's atmosphere. So I asked for a calculation for less dense gas clouds.
CAPTURE TIME & DISTANCE FOR THINNER GAS CLOUDS
To determine the deceleration time and distance for a Jupiter-sized planet moving through a gas cloud with a density that is 10% of the previously assumed value, we will follow a similar approach as before, adjusting the calculations based on the new density.
{I'm skipping the calculations.}
Summary of Results with Adjusted Density
Time to Slow Down for Capture: Approximately 16.9 hours.
Distance Traveled During Deceleration: Approximately 8,922 km.
The time seems plausible, but the distance is way wrong again. I explained the error like I did earlier, but it came up with 8,917 km, almost the same as before. So I said: Dope. Can't you see you keep coming up with the wrong distance that's way too short? Find the average speed between the initial velocity and the final velocity and multiply that by the time to get the distance. I found that its error was converting meters to kilometers properly. Finally, it did it correctly, I assume, as follows.
I apologize for the repeated errors in my previous responses. Thank you for your patience. Here’s the corrected summary with the accurate distance stated clearly:
Summary of Results with Adjusted Density
Time to Slow Down for Capture: Approximately 16.9 hours.
Distance Traveled During Deceleration: Approximately 8,917,000,000 meters, or 8,917,000 kilometers.
CAPTURE TIME & DISTANCE IN MUCH THINNER GAS CLOUD
Those answers look a bit plausible. But then I switched to Copilot, since Perplexity stopped answering. I said: If a Jupiter-size rogue planet traveling at 200 km/s encountered a stationary gas cloud 1% as dense as Earth's atmosphere, how long a time and distance would it take to reduce to 100 km/s?
Calculating this involves a lot of physics. Here’s a simplified approach:
1. Mass of Jupiter: 1.898×10^27kg
2. Initial Velocity: 200 km/s
3. Final Velocity: 100 km/s
4. Density of Gas Cloud: 1% of Earth's atmosphere (1.225 kg/m^3) = 0.01225 kg/m^3
Using the concept of drag force, assuming the planet loses velocity primarily due to the drag force from the gas cloud:
The drag force is given by:
F_d=1/2(ρv^2C_dA)
where:
ρ = density of the gas cloud
v = velocity of the planet
C_d = drag coefficient (let's assume C_d = 2.2 for a rough sphere)
A = cross-sectional area of Jupiter
The cross-sectional area A is:
A=πr^2
… The loss in kinetic energy (ΔKE) will be equal to the work done by the drag force:
ΔKE=W=F_d⋅d
… d≈6.59 billion kilometers
… t≈1.38 years
6,590,000,000km/778,500,000km ≈ 8.47 times around Jupiter's orbit. Jupiter now takes almost 12 years to orbit once, so in 8.5 orbits, it would take over 100 years. So it needs to slow down a lot more to reach its present orbital speed. I then asked Copilot to calculate for a ten times greater density gas cloud, to compare with Perplexity. After calculation it said this.
If the gas cloud density were ten times greater, it would take approximately 50.8 days and 659 million kilometers for the rogue planet to reduce its speed from 200 km/s to 100 km/s.
So that would be a little under one Jupiter orbit, i.e. about 85% of one orbit. I don't imagine a gas cloud 10% of Earth's atmosphere density was likely, but if it remained in place for a few years, Jupiter could have slowed to its present speed in a few years. Same applies to Saturn. Electric charges on the cloud and the planet could have helped a lot too.
Perplexity said 17 hours, 9 million km to reduce speed in ~10% Earth's atmosphere density for the gas cloud.
Copilot said 51 days, 660 million km. I'm guessing Copilot has the better estimate.