Minimum safe distance to black hole

[Passionflower]

Furthermore, almost of that relative velocity will be due to the motion of the Earth and not the black hole.

This does not make sense, all inertial motion is relative.

 

[Tracer]

This does not make sense, all inertial motion is relative.

This is similar to the resolution of the "Twin Paradox" which is resolved by recognizing that one twin has been accelarated to a higher speed than the stay at home twin. If the Black hole is considered to be the stay at home twin and the solar system is considered to be the accelerated twin it should be obvious that the gravitational attraction between the black hole and the solar system will cause the black hole's velocity to change very little while the velocity of the solar system will change by comparitivly large amount.

Let the 18 billion solar mass black hole be moving through the milkyway galaxy with a relative velocity of 1000 km/second with the galactic center. If the Earth's solar system has been free falling toward the black hole for thousands of years, the relative velocity now of Earth with the black hole would be approximately equal to the escape velocity at the Earth's present distance to the black hole.

At the present distance in the scenario in my posts, the escape velocity is 6.65E07 meters/second. That means the Earth could have almost as much as 6.65E07 meters/second relative velocity with other distant objects in the milky way galaxy if they have not been affected very much by the gravity of the black hole.

Therefore, in the scenario of these posts, if ships launched from the Earth could perform a sling shot maneuver around the Black hole, those ships could redirect their ship's initial relative speed (6.65E07 meters/second) to nearly that same speed but in a direction toward a distant promising destinaton.

 

[Passionflower]

This is similar to the resolution of the "Twin Paradox" which is resolved by recognizing that one twin has been accelarated to a higher speed than the stay at home twin. If the Black hole is considered to be the stay at home twin and the solar system is considered to be the accelerated twin it should be obvious that the gravitational attraction between the black hole and the solar system will cause the black hole's velocity to change very little while the velocity of the solar system will change by comparitivly large amount.

Both the black hole and the solar system do not undergo any proper acceleration. Your comparison with the twin experiment does not make any sense her.

I strongly suggest you go back to the basics and try to understand that all velocity is relative. Both in SR and GR.

 

[Tracer]

Both the black hole and the solar system do not undergo any proper acceleration. Your comparison with the twin experiment does not make any sense her.

I strongly suggest you go back to the basics and try to understand that all velocity is relative. Both in SR and GR.

From your "proper acceleration" link Passionflower.
"In relativity theory, proper acceleration[1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured."

Given the center of the milky way galaxy, the 18 billion solar mass black hole and the free falling solar system as three colinear points with the black hole between the solar system and the galactic center. Why wouldn't the relative velocity between the black hole and the solar system increase with time and be approximately equal to the escape velocity from the black hole at any given distance from the black hole? I have tried to use numbers to prove my point. Please don't just flip me off with relativity dogma. That does not help me at all to understand your reponses.

For instance in one of your earlier posts you said that only a small and short acceleration period would be required to swerve a ship around the black hole in the scenario that I have been using. Can you show the amount and duration of the acceleration required to accomplish this? I agree that it could be done. However I might not agree with what you consider to be only a short period of acceleration.

 

[Passionflower]

When the velocity between two free falling objects changes it is due to spacetime curvature not due to a force. Proper acceleration requires a force.

I can do the calculations but since I feel I am the only one on this forum sticking out his neck to do GR calculations I let someone else do it this time., but I would not hold my breath, there are too many 'experts' on this forum who do not bother showing calculations.

 

[Tracer]

I'm guessing anything landing in the stable orbits would be completely ripped apart? So the orbits might be filled with rings of matter like a planet?

I guess a slightly more interesting question for me is how big a black hole could pass near our solar system without disrupting our orbits around the sun? Does information on such a scenario?

Here are some numbers to consider in answer to your question. If a three solar mass black hole cruised tangentially by the solar system at a speed of 1000 km per second and at a minimum distance of 2 light years the orbits of the planets would be changed very little in the short term by the presence of the black hole. However, the black hole would have more influence than the sun on Oort cloud objects. Consequenty a large portion of the Oort cloud objects could be captured by the black hole and carried away. The loss of the mass of the captured Oort cloud objects could affect the planet's orbits over a long period of time. The total mass and size of the Oort cloud is conjecture. I don't know any way to estimate the long term effect on the loss of some of its mass on the orbits of the planet's.

Mass of sun 1.99E+30 kilograms
Universal G 6.67E-11
lightspeed 299792458 meters/sec
1 mile = 1609 meters 1609 meters
1 AU = 93,000,000 miles 93000000 miles
1 AU =1609*93000000 meters 1.49637E+11 meters
1 LY = 299792358*365*24*60*60 meters 9.45425E+15 meters
Mass of black hole = 3 solar masses 5.97E+30 kilograms

Acc sun on Earth =GM/R^2 @ R =1 au 5.9284853618E-03 meters/sec/sec
Acc Bh on Earth = G(Mbh)/Rbh) @R =2 ly -1 au 1.1138719171E-12 meters/sec/sec
estimate of delta vel Earth in 10000 yrs 3.5127064777E-01 meters /sec
earth orbital vel sqrt(GM/r) 2.9784572585E+04 meters/sec
centrifugal acc of Earth =v^2/R 5.9284853618E-03 meters/sec/sec
Acc sun on far oort cloud objects 1.49E-12 meters/sec/sec
Acc Bh on far oort cloud objects 4.46E-12 meters/sec/sec
Acc sun on outer Kyper & oort at 55 au's 1.95983E-06 meters/sec/sec
Acc Bh on outer kyper & oort 55 au's from sun 1.11482E-12 meters/sec/sec

 

[Tracer]

Here are some numbers to consider in answer to your question. If a three solar mass black hole cruised tangentially by the solar system at a speed of 1000 km per second and at a minimum distance of 2 light years the orbits of the planets would be changed very little in the short term by the presence of the black hole. However, the black hole would have more influence than the sun on Oort cloud objects. Consequenty a large portion of the Oort cloud objects could be captured by the black hole and carried away. The loss of the mass of the captured Oort cloud objects could affect the planet's orbits over a long period of time. The total mass and size of the Oort cloud is conjecture. I don't know any way to estimate the long term effect on the loss of some of its mass on the orbits of the planet's.

Mass of sun 1.99E+30 kilograms
Universal G 6.67E-11
lightspeed 299792458 meters/sec
1 mile = 1609 meters 1609 meters
1 AU = 93,000,000 miles 93000000 miles
1 AU =1609*93000000 meters 1.49637E+11 meters
1 LY = 299792358*365*24*60*60 meters 9.45425E+15 meters
Mass of black hole = 3 solar masses 5.97E+30 kilograms

Acc sun on Earth =GM/R^2 @ R =1 au 5.9284853618E-03 meters/sec/sec
Acc Bh on Earth = G(Mbh)/Rbh) @R =2 ly -1 au 1.1138719171E-12 meters/sec/sec
estimate of delta vel Earth in 10000 yrs 3.5127064777E-01 meters /sec
earth orbital vel sqrt(GM/r) 2.9784572585E+04 meters/sec
centrifugal acc of Earth =v^2/R 5.9284853618E-03 meters/sec/sec
Acc sun on far oort cloud objects 1.49E-12 meters/sec/sec
Acc Bh on far oort cloud objects 4.46E-12 meters/sec/sec
Acc sun on outer Kyper & oort at 55 au's 1.95983E-06 meters/sec/sec
Acc Bh on outer kyper & oort 55 au's from sun 1.11482E-12 meters/sec/sec

Note this forum's software removed all of the white space from my post and renders if useless.

 

[George Jones]

Note this forum's software removed all of the white space from my post and renders if useless.

Get the spacing correct in Notepad, then copy it here, putting it between code /code tags. Like this:

A    =          B

 

[PAllen]

Note this forum's software removed all of the white space from my post and renders if useless.

Actually, I had no trouble reading it, and thought it was interesting.

 

[Tracer]

If a three solar mass black hole cruised tangentially by the solar system at a speed of 1000 km per second and at a minimum distance of 2 light years the orbits of the planets would be changed very little in the short term by the presence of the black hole. However, the black hole would have more influence than the sun on Oort cloud objects. Consequenty a large portion of the Oort cloud objects could be captured by the black hole and carried away. The loss of the mass of the captured Oort cloud objects could affect the planet's orbits over a long period of time. The total mass and size of the Oort cloud is conjecture. I don't know any way to estimate the long term effect on the loss of some of its mass on the orbits of the planet's.
The Oort cloud is thought to surround the solar system in a spherical mass extending out to as much as three light years from the sun. If the mass of the bodies in the Oort cloud is evenly distributed around a shell at any given distance from the sun, then the gravitational effects of the mass in that shell will cancel for all other bodies within that shell.
If all of the Oort cloud mass is distributed in this way, then the sun and all planets will be totally unaffected by the Oort cloud. However if the 3 solar mass black hole cruises by the solar system tangentially and at a distance of one light year from the sun, nearly one entire hemisphere of the Oort cloud could be captured and carried away by the black hole. In this case, the sun and the planets would be affected by the half of the mass of the original Oort cloud in the remaining hemisphere. At the very least, the planetary orbits would probably become more eccentric in the long term.