{
    "metadata": {
        "calculation_date": "2025-09-25T17:14:40.417617",
        "author": "Yoshiyuki Matsuyama",
        "article": "#006 Disappearance Time",
        "version": "1.0"
    },
    "physical_constants": {
        "G": 6.6743e-11,
        "c": 299792458,
        "M_sun": 1.98847e+30
    },
    "black_hole_parameters": {
        "M87": {
            "mass_solar": 6500000000,
            "schwarzschild_radius": 19196705983434.707
        },
        "SgrA": {
            "mass_solar": 4300000,
            "schwarzschild_radius": 12699359342.887577
        }
    },
    "results": {
        "different_radii": {
            "description": "Disappearance time for various tube radii",
            "calculations": [
                {
                    "r_meters": 9598352991717.354,
                    "delta_t_seconds": 201166.60336625847,
                    "delta_t_minutes": 3352.7767227709746,
                    "delta_t_hours": 55.879612046182906,
                    "delta_t_days": 2.3283171685909543,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 0.5,
                    "r_km": 9598352991.717354,
                    "r_AU": 64.16011358099836
                },
                {
                    "r_meters": 19196705983434.707,
                    "delta_t_seconds": 402333.20673251693,
                    "delta_t_minutes": 6705.553445541949,
                    "delta_t_hours": 111.75922409236581,
                    "delta_t_days": 4.656634337181909,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 1,
                    "r_km": 19196705983.434708,
                    "r_AU": 128.3202271619967
                },
                {
                    "r_meters": 38393411966869.414,
                    "delta_t_seconds": 804666.4134650339,
                    "delta_t_minutes": 13411.106891083899,
                    "delta_t_hours": 223.51844818473162,
                    "delta_t_days": 9.313268674363817,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 2,
                    "r_km": 38393411966.869415,
                    "r_AU": 256.6404543239934
                },
                {
                    "r_meters": 67188470942021.48,
                    "delta_t_seconds": 1408166.2235638094,
                    "delta_t_minutes": 23469.437059396823,
                    "delta_t_hours": 391.1572843232804,
                    "delta_t_days": 16.29822018013668,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 3.5,
                    "r_km": 67188470942.02148,
                    "r_AU": 449.1207950669885
                },
                {
                    "r_meters": 95983529917173.53,
                    "delta_t_seconds": 2011666.0336625846,
                    "delta_t_minutes": 33527.767227709744,
                    "delta_t_hours": 558.7961204618291,
                    "delta_t_days": 23.283171685909544,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 5,
                    "r_km": 95983529917.17354,
                    "r_AU": 641.6011358099835
                },
                {
                    "r_meters": 191967059834347.06,
                    "delta_t_seconds": 4023332.067325169,
                    "delta_t_minutes": 67055.53445541949,
                    "delta_t_hours": 1117.5922409236582,
                    "delta_t_days": 46.56634337181909,
                    "formula": "Δt = 2πr\/c",
                    "r_Rs_units": 10,
                    "r_km": 191967059834.34708,
                    "r_AU": 1283.202271619967
                }
            ]
        },
        "observation_windows": {
            "standard_radius": 19196705983434.707,
            "period_hours": 111.75922409236581,
            "windows": [
                {
                    "cycle": 1,
                    "disappear_UTC": "2025-01-01T00:00:00",
                    "reappear_UTC": "2025-01-03T07:52:46.603366",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 2,
                    "disappear_UTC": "2025-01-05T15:45:33.206733",
                    "reappear_UTC": "2025-01-07T23:38:19.810099",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 3,
                    "disappear_UTC": "2025-01-10T07:31:06.413465",
                    "reappear_UTC": "2025-01-12T15:23:53.016831",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 4,
                    "disappear_UTC": "2025-01-14T23:16:39.620198",
                    "reappear_UTC": "2025-01-17T07:09:26.223564",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 5,
                    "disappear_UTC": "2025-01-19T15:02:12.826930",
                    "reappear_UTC": "2025-01-21T22:54:59.430296",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 6,
                    "disappear_UTC": "2025-01-24T06:47:46.033663",
                    "reappear_UTC": "2025-01-26T14:40:32.637029",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 7,
                    "disappear_UTC": "2025-01-28T22:33:19.240395",
                    "reappear_UTC": "2025-01-31T06:26:05.843761",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 8,
                    "disappear_UTC": "2025-02-02T14:18:52.447128",
                    "reappear_UTC": "2025-02-04T22:11:39.050494",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 9,
                    "disappear_UTC": "2025-02-07T06:04:25.653860",
                    "reappear_UTC": "2025-02-09T13:57:12.257226",
                    "duration_hours": 55.879612046182906
                },
                {
                    "cycle": 10,
                    "disappear_UTC": "2025-02-11T21:49:58.860593",
                    "reappear_UTC": "2025-02-14T05:42:45.463959",
                    "duration_hours": 55.879612046182906
                }
            ]
        },
        "black_hole_comparison": {
            "M87": {
                "mass_solar": 6500000000,
                "Rs_meters": 19196705983434.707,
                "Rs_km": 19196705983.434708,
                "delta_t_seconds": 402333.20673251693,
                "delta_t_hours": 111.75922409236581,
                "delta_t_days": 4.656634337181909
            },
            "SgrA": {
                "mass_solar": 4300000,
                "Rs_meters": 12699359342.887577,
                "Rs_km": 12699359.342887577,
                "delta_t_seconds": 266.15889060766506,
                "delta_t_hours": 0.07393302516879585,
                "delta_t_minutes": 4.435981510127751
            },
            "ratio": {
                "mass_ratio": 1511.6279069767443,
                "Rs_ratio": 1511.627906976744,
                "time_ratio": 1511.627906976744
            }
        },
        "detectability": {
            "time_resolution_required": {
                "ideal_hours": 1,
                "minimum_hours": 6,
                "description": "To detect disappearance\/reappearance transitions"
            },
            "observation_duration": {
                "minimum_cycles": 3,
                "minimum_days": 13.969903011545728,
                "recommended_days": 46.56634337181909
            },
            "instruments": {
                "ALMA": {
                    "suitable": true,
                    "time_resolution": "< 1 hour achievable",
                    "challenges": "Weather, scheduling"
                },
                "EHT": {
                    "suitable": false,
                    "reason": "Campaign mode, not continuous monitoring"
                },
                "X-ray": {
                    "suitable": true,
                    "satellites": [
                        "Chandra",
                        "XMM-Newton",
                        "NuSTAR"
                    ],
                    "advantage": "Continuous monitoring possible"
                }
            },
            "signatures": {
                "flux_variation": "Periodic dimming\/brightening",
                "spectral_change": "Possible hardening during transit",
                "polarization": "Rotation pattern change"
            }
        },
        "relativistic_corrections": {
            "description": "General relativistic time dilation effects",
            "corrections": [
                {
                    "r_Rs": 2,
                    "gravitational_redshift": -0.2928932188134524,
                    "time_dilation_factor": 0.7071067811865476,
                    "delta_t_proper_seconds": 80466.64134650338,
                    "delta_t_observed_seconds": 113797.01551083672,
                    "correction_percent": 41.421356237309496
                },
                {
                    "r_Rs": 3,
                    "gravitational_redshift": -0.18350341907227397,
                    "time_dilation_factor": 0.816496580927726,
                    "delta_t_proper_seconds": 120699.9620197551,
                    "delta_t_observed_seconds": 147826.65946085463,
                    "correction_percent": 22.474487139158896
                },
                {
                    "r_Rs": 5,
                    "gravitational_redshift": -0.10557280900008414,
                    "time_dilation_factor": 0.8944271909999159,
                    "delta_t_proper_seconds": 201166.60336625847,
                    "delta_t_observed_seconds": 224911.09996484598,
                    "correction_percent": 11.80339887498949
                },
                {
                    "r_Rs": 10,
                    "gravitational_redshift": -0.05131670194948623,
                    "time_dilation_factor": 0.9486832980505138,
                    "delta_t_proper_seconds": 402333.20673251693,
                    "delta_t_observed_seconds": 424096.43719804817,
                    "correction_percent": 5.409255338945984
                },
                {
                    "r_Rs": 20,
                    "gravitational_redshift": -0.025320565519103666,
                    "time_dilation_factor": 0.9746794344808963,
                    "delta_t_proper_seconds": 804666.4134650339,
                    "delta_t_observed_seconds": 825570.3208651268,
                    "correction_percent": 2.59783520851542
                },
                {
                    "r_Rs": 50,
                    "gravitational_redshift": -0.01005050633883342,
                    "time_dilation_factor": 0.9899494936611666,
                    "delta_t_proper_seconds": 2011666.0336625846,
                    "delta_t_observed_seconds": 2032089.562693513,
                    "correction_percent": 1.0152544552210596
                }
            ]
        },
        "visualization": {
            "file": "disappearance_time_006.html",
            "type": "disappearance_time_vs_radius"
        }
    }
}