Star System Generated (Seed: 1766389577)

Star Details

Spectral Class: M8V

Temperature: 2,617 K

Mass: 0.28 sol

Luminosity: 0.01 lux

Habitable Zone (HZ)

Inner Boundary: 0.1 AU

Outer Boundary: 0.14 AU

Physical Limits

Snow Line: 0.48 AU

Max System Radius: 10.6 AU

Planetary System (7 Planets)

Asteroid Belt

Center: 0.28 AU

Composition

Type: Inner (Rocky/Metallic)

A dense region of planetesimals and debris.

Boundary

Planet 1 - Gas Giant

Semi-Major Axis: 0.55 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 874.2

Radius: 13.5

Gravity: 4.8 G

Time & Orbit

Eccentricity (e): 0.041

Orbit Range: 0.53 AU - 0.57 AU

Year: 282 Days

Day: 9.9 Hours

Environment

Temp: -155 °C

Axial Tilt: 36.7 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (34)

Outer Limit: 66,165,022 km

  • M1: 168,597 km (0.092 R)
  • M2: 289,173 km (0.072 R)
  • M3: 390,600 km (0.089 R)
  • M4: 476,320 km (0.104 R)
  • M5: 614,847 km (0.1 R)
  • M6: 751,879 km (0.081 R)
  • M7: 885,619 km (0.034 R)
  • M8: 981,063 km (0.119 R)
  • M9: 1,080,396 km (0.079 R)
  • M10: 1,179,280 km (0.068 R)
  • M11: 1,272,928 km (0.076 R)
  • M12: 1,360,443 km (0.096 R)
  • M13: 1,621,491 km (0.092 R)
  • M14: 1,712,297 km (0.085 R)
  • M15: 1,804,898 km (0.114 R)
  • M16: 1,974,991 km (0.083 R)
  • M17: 2,198,042 km (0.104 R)
  • M18: 2,320,861 km (0.083 R)
  • M19: 2,584,752 km (0.088 R)
  • M20: 2,669,275 km (0.115 R)
  • M21: 2,771,899 km (0.106 R)
  • M22: 3,046,561 km (0.116 R)
  • M23: 3,172,223 km (0.116 R)
  • M24: 3,391,683 km (0.09 R)
  • M25: 3,521,983 km (0.112 R)
  • M26: 3,673,077 km (0.112 R)
  • M27: 3,826,414 km (0.111 R)
  • M28: 4,034,206 km (0.103 R)
  • M29: 4,139,523 km (0.069 R)
  • M30: 4,225,841 km (0.103 R)
  • M31: 4,346,267 km (0.106 R)
  • M32: 4,495,117 km (0.115 R)
  • M33: 4,652,494 km (0.116 R)
  • M34: 4,756,165 km (0.077 R)

Planet 2 - Gas Giant

Semi-Major Axis: 0.62 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 853.3

Radius: 14.6

Gravity: 4 G

Time & Orbit

Eccentricity (e): 0.176

Orbit Range: 0.51 AU - 0.73 AU

Year: 337 Days

Day: 5.3 Hours

Environment

Temp: -152 °C

Axial Tilt: 38 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (38)

Outer Limit: 66,165,022 km

  • M1: 191,186 km (0.111 R)
  • M2: 328,966 km (0.045 R)
  • M3: 526,884 km (0.087 R)
  • M4: 721,660 km (0.107 R)
  • M5: 823,686 km (0.114 R)
  • M6: 915,090 km (0.088 R)
  • M7: 1,006,195 km (0.088 R)
  • M8: 1,100,741 km (0.068 R)
  • M9: 1,203,216 km (0.102 R)
  • M10: 1,337,555 km (0.12 R)
  • M11: 1,438,084 km (0.105 R)
  • M12: 1,546,543 km (0.075 R)
  • M13: 1,730,099 km (0.047 R)
  • M14: 1,840,802 km (0.095 R)
  • M15: 2,064,002 km (0.086 R)
  • M16: 2,221,828 km (0.055 R)
  • M17: 2,313,830 km (0.098 R)
  • M18: 2,418,998 km (0.092 R)
  • M19: 2,519,827 km (0.116 R)
  • M20: 2,731,956 km (0.105 R)
  • M21: 2,868,539 km (0.077 R)
  • M22: 2,962,935 km (0.115 R)
  • M23: 3,064,812 km (0.031 R)
  • M24: 3,187,482 km (0.052 R)
  • M25: 3,324,813 km (0.094 R)
  • M26: 3,451,073 km (0.098 R)
  • M27: 3,558,485 km (0.092 R)
  • M28: 3,839,130 km (0.111 R)
  • M29: 4,063,377 km (0.107 R)
  • M30: 4,220,006 km (0.1 R)
  • M31: 4,349,708 km (0.047 R)
  • M32: 4,642,920 km (0.082 R)
  • M33: 4,739,560 km (0.104 R)
  • M34: 4,844,428 km (0.063 R)
  • M35: 4,957,673 km (0.093 R)
  • M36: 5,079,446 km (0.08 R)
  • M37: 5,194,636 km (0.116 R)
  • M38: 5,287,387 km (0.077 R)

Planet 3 - Gas Giant

Semi-Major Axis: 0.67 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 735.3

Radius: 14.5

Gravity: 3.5 G

Time & Orbit

Eccentricity (e): 0.19

Orbit Range: 0.54 AU - 0.8 AU

Year: 379 Days

Day: 14.8 Hours

Environment

Temp: -157 °C

Axial Tilt: 9.9 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (37)

Outer Limit: 66,165,022 km

  • M1: 186,549 km (0.118 R)
  • M2: 315,352 km (0.032 R)
  • M3: 434,133 km (0.115 R)
  • M4: 575,503 km (0.111 R)
  • M5: 673,490 km (0.095 R)
  • M6: 910,602 km (0.072 R)
  • M7: 1,007,691 km (0.029 R)
  • M8: 1,099,694 km (0.038 R)
  • M9: 1,208,900 km (0.089 R)
  • M10: 1,302,997 km (0.115 R)
  • M11: 1,394,851 km (0.094 R)
  • M12: 1,570,179 km (0.101 R)
  • M13: 1,861,297 km (0.057 R)
  • M14: 2,050,239 km (0.092 R)
  • M15: 2,216,592 km (0.095 R)
  • M16: 2,316,224 km (0.103 R)
  • M17: 2,453,555 km (0.109 R)
  • M18: 2,637,111 km (0.118 R)
  • M19: 2,959,644 km (0.113 R)
  • M20: 3,070,048 km (0.037 R)
  • M21: 3,181,947 km (0.105 R)
  • M22: 3,301,924 km (0.031 R)
  • M23: 3,560,130 km (0.063 R)
  • M24: 3,719,901 km (0.117 R)
  • M25: 3,825,367 km (0.105 R)
  • M26: 3,917,519 km (0.114 R)
  • M27: 4,053,654 km (0.03 R)
  • M28: 4,169,592 km (0.111 R)
  • M29: 4,345,519 km (0.11 R)
  • M30: 4,509,029 km (0.062 R)
  • M31: 4,629,306 km (0.069 R)
  • M32: 4,727,891 km (0.091 R)
  • M33: 4,873,151 km (0.117 R)
  • M34: 4,996,569 km (0.055 R)
  • M35: 5,207,352 km (0.103 R)
  • M36: 5,341,691 km (0.109 R)
  • M37: 5,485,006 km (0.081 R)

Planet 4 - Gas Giant

Semi-Major Axis: 1.09 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 562.7

Radius: 10.5

Gravity: 5.1 G

Time & Orbit

Eccentricity (e): 0.16

Orbit Range: 0.92 AU - 1.26 AU

Year: 786 Days

Day: 13.9 Hours

Environment

Temp: -185 °C

Axial Tilt: 10.5 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (52)

Outer Limit: 66,165,022 km

  • M1: 155,283 km (0.116 R)
  • M2: 252,671 km (0.079 R)
  • M3: 331,359 km (0.04 R)
  • M4: 528,080 km (0.072 R)
  • M5: 639,531 km (0.027 R)
  • M6: 817,702 km (0.089 R)
  • M7: 949,647 km (0.059 R)
  • M8: 1,083,238 km (0.12 R)
  • M9: 1,273,676 km (0.102 R)
  • M10: 1,370,017 km (0.063 R)
  • M11: 1,488,798 km (0.096 R)
  • M12: 1,570,030 km (0.082 R)
  • M13: 1,673,701 km (0.117 R)
  • M14: 1,851,722 km (0.119 R)
  • M15: 1,961,677 km (0.069 R)
  • M16: 2,104,094 km (0.109 R)
  • M17: 2,172,909 km (0.051 R)
  • M18: 2,383,543 km (0.082 R)
  • M19: 2,479,435 km (0.111 R)
  • M20: 2,601,208 km (0.093 R)
  • M21: 2,666,881 km (0.104 R)
  • M22: 2,918,505 km (0.091 R)
  • M23: 3,151,578 km (0.095 R)
  • M24: 3,248,368 km (0.064 R)
  • M25: 3,399,761 km (0.079 R)
  • M26: 3,544,572 km (0.041 R)
  • M27: 3,663,652 km (0.097 R)
  • M28: 3,746,978 km (0.109 R)
  • M29: 3,830,902 km (0.085 R)
  • M30: 3,906,000 km (0.106 R)
  • M31: 3,972,123 km (0.118 R)
  • M32: 4,386,808 km (0.082 R)
  • M33: 4,495,117 km (0.093 R)
  • M34: 4,644,266 km (0.1 R)
  • M35: 4,998,813 km (0.102 R)
  • M36: 5,143,175 km (0.085 R)
  • M37: 5,278,411 km (0.037 R)
  • M38: 5,435,938 km (0.09 R)
  • M39: 5,552,475 km (0.116 R)
  • M40: 5,669,759 km (0.115 R)
  • M41: 5,755,628 km (0.096 R)
  • M42: 5,831,175 km (0.087 R)
  • M43: 5,939,634 km (0.107 R)
  • M44: 6,070,682 km (0.114 R)
  • M45: 6,191,557 km (0.099 R)
  • M46: 6,380,050 km (0.106 R)
  • M47: 6,525,609 km (0.076 R)
  • M48: 6,593,077 km (0.105 R)
  • M49: 6,694,804 km (0.074 R)
  • M50: 6,796,979 km (0.079 R)
  • M51: 7,141,653 km (0.117 R)
  • M52: 7,269,409 km (0.025 R)

Planet 5 - Gas Giant

Semi-Major Axis: 1.34 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 409.8

Radius: 8.7

Gravity: 5.41 G

Time & Orbit

Eccentricity (e): 0.215

Orbit Range: 1.05 AU - 1.63 AU

Year: 1071 Days

Day: 14.3 Hours

Environment

Temp: -183 °C

Axial Tilt: 3.6 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (65)

Outer Limit: 66,165,022 km

  • M1: 119,977 km (0.116 R)
  • M2: 197,020 km (0.082 R)
  • M3: 289,322 km (0.094 R)
  • M4: 355,295 km (0.064 R)
  • M5: 414,386 km (0.082 R)
  • M6: 486,941 km (0.061 R)
  • M7: 559,496 km (0.109 R)
  • M8: 620,532 km (0.101 R)
  • M9: 711,338 km (0.082 R)
  • M10: 883,076 km (0.069 R)
  • M11: 1,036,713 km (0.107 R)
  • M12: 1,113,756 km (0.104 R)
  • M13: 1,294,321 km (0.096 R)
  • M14: 1,434,344 km (0.081 R)
  • M15: 1,564,644 km (0.096 R)
  • M16: 1,744,760 km (0.12 R)
  • M17: 1,829,582 km (0.089 R)
  • M18: 1,884,335 km (0.028 R)
  • M19: 1,971,550 km (0.062 R)
  • M20: 2,141,643 km (0.111 R)
  • M21: 2,216,143 km (0.119 R)
  • M22: 2,663,291 km (0.071 R)
  • M23: 2,788,504 km (0.087 R)
  • M24: 3,044,765 km (0.112 R)
  • M25: 3,100,715 km (0.107 R)
  • M26: 3,318,380 km (0.103 R)
  • M27: 3,375,975 km (0.103 R)
  • M28: 3,482,489 km (0.105 R)
  • M29: 3,669,187 km (0.08 R)
  • M30: 3,738,750 km (0.091 R)
  • M31: 4,052,307 km (0.107 R)
  • M32: 4,269,523 km (0.096 R)
  • M33: 4,342,826 km (0.058 R)
  • M34: 4,416,578 km (0.05 R)
  • M35: 4,618,685 km (0.106 R)
  • M36: 4,683,161 km (0.104 R)
  • M37: 4,813,012 km (0.082 R)
  • M38: 4,878,536 km (0.099 R)
  • M39: 4,966,201 km (0.068 R)
  • M40: 5,131,955 km (0.085 R)
  • M41: 5,198,825 km (0.087 R)
  • M42: 5,254,625 km (0.097 R)
  • M43: 5,344,534 km (0.079 R)
  • M44: 5,571,623 km (0.067 R)
  • M45: 5,790,186 km (0.101 R)
  • M46: 6,070,382 km (0.105 R)
  • M47: 6,271,442 km (0.033 R)
  • M48: 6,414,906 km (0.092 R)
  • M49: 6,498,980 km (0.089 R)
  • M50: 6,777,980 km (0.06 R)
  • M51: 6,839,166 km (0.102 R)
  • M52: 6,900,501 km (0.115 R)
  • M53: 7,210,019 km (0.098 R)
  • M54: 7,347,649 km (0.092 R)
  • M55: 7,600,170 km (0.115 R)
  • M56: 7,676,465 km (0.094 R)
  • M57: 7,906,995 km (0.077 R)
  • M58: 8,010,218 km (0.057 R)
  • M59: 8,087,859 km (0.116 R)
  • M60: 8,165,800 km (0.081 R)
  • M61: 8,309,264 km (0.067 R)
  • M62: 8,718,414 km (0.088 R)
  • M63: 8,824,928 km (0.058 R)
  • M64: 8,891,798 km (0.056 R)
  • M65: 9,079,992 km (0.119 R)

Planet 6 - Ice Giant

Semi-Major Axis: 7.72 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 277.9

Radius: 3

Gravity: 30.88 G

Time & Orbit

Eccentricity (e): 0.111

Orbit Range: 6.86 AU - 8.58 AU

Year: 14806 Days

Day: 15.1 Hours

Environment

Temp: -227 °C

Axial Tilt: 38.5 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (80)

Outer Limit: 66,165,022 km

  • M1: 64,327 km (0.074 R)
  • M2: 219,310 km (0.093 R)
  • M3: 419,622 km (0.107 R)
  • M4: 552,315 km (0.106 R)
  • M5: 765,642 km (0.091 R)
  • M6: 1,040,603 km (0.118 R)
  • M7: 1,099,096 km (0.081 R)
  • M8: 1,343,538 km (0.084 R)
  • M9: 1,694,794 km (0.088 R)
  • M10: 1,951,953 km (0.081 R)
  • M11: 1,999,974 km (0.05 R)
  • M12: 2,121,896 km (0.096 R)
  • M13: 2,246,212 km (0.072 R)
  • M14: 2,321,909 km (0.091 R)
  • M15: 2,501,875 km (0.048 R)
  • M16: 2,606,743 km (0.116 R)
  • M17: 2,713,107 km (0.039 R)
  • M18: 3,761,788 km (0.098 R)
  • M19: 4,343,574 km (0.119 R)
  • M20: 4,374,990 km (0.11 R)
  • M21: 5,217,375 km (0.117 R)
  • M22: 5,385,075 km (0.085 R)
  • M23: 5,968,207 km (0.107 R)
  • M24: 6,355,965 km (0.116 R)
  • M25: 6,643,193 km (0.048 R)
  • M26: 7,417,062 km (0.119 R)
  • M27: 7,529,859 km (0.1 R)
  • M28: 7,605,406 km (0.068 R)
  • M29: 8,102,669 km (0.059 R)
  • M30: 8,570,911 km (0.095 R)
  • M31: 8,848,116 km (0.057 R)
  • M32: 9,087,921 km (0.112 R)
  • M33: 9,208,796 km (0.083 R)
  • M34: 9,411,202 km (0.098 R)
  • M35: 10,403,186 km (0.064 R)
  • M36: 11,820,476 km (0.113 R)
  • M37: 12,350,651 km (0.09 R)
  • M38: 12,395,231 km (0.107 R)
  • M39: 12,484,541 km (0.068 R)
  • M40: 13,342,784 km (0.097 R)
  • M41: 13,479,965 km (0.038 R)
  • M42: 13,894,501 km (0.119 R)
  • M43: 14,173,201 km (0.099 R)
  • M44: 14,594,619 km (0.119 R)
  • M45: 14,830,684 km (0.1 R)
  • M46: 15,980,493 km (0.11 R)
  • M47: 16,126,351 km (0.033 R)
  • M48: 16,762,890 km (0.084 R)
  • M49: 16,910,992 km (0.108 R)
  • M50: 18,721,575 km (0.064 R)
  • M51: 19,390,427 km (0.084 R)
  • M52: 19,493,949 km (0.096 R)
  • M53: 19,805,860 km (0.074 R)
  • M54: 19,857,921 km (0.105 R)
  • M55: 20,487,129 km (0.097 R)
  • M56: 21,764,994 km (0.083 R)
  • M57: 24,173,969 km (0.078 R)
  • M58: 24,676,917 km (0.1 R)
  • M59: 25,466,195 km (0.049 R)
  • M60: 25,522,893 km (0.027 R)
  • M61: 25,807,129 km (0.12 R)
  • M62: 31,339,557 km (0.108 R)
  • M63: 31,765,612 km (0.111 R)
  • M64: 32,316,431 km (0.025 R)
  • M65: 32,746,974 km (0.053 R)
  • M66: 35,813,281 km (0.101 R)
  • M67: 36,258,784 km (0.108 R)
  • M68: 36,770,109 km (0.091 R)
  • M69: 38,643,673 km (0.114 R)
  • M70: 39,296,817 km (0.112 R)
  • M71: 40,349,538 km (0.075 R)
  • M72: 40,746,720 km (0.115 R)
  • M73: 40,879,413 km (0.104 R)
  • M74: 41,278,391 km (0.108 R)
  • M75: 41,678,565 km (0.109 R)
  • M76: 43,495,132 km (0.07 R)
  • M77: 44,310,889 km (0.101 R)
  • M78: 44,925,886 km (0.115 R)
  • M79: 45,543,875 km (0.11 R)
  • M80: 45,957,363 km (0.104 R)

Asteroid Belt

Center: 8.76 AU

Composition

Type: Outer System (Icy)

A dense region of planetesimals and debris.

Boundary

Planet 7 - Ice Giant

Semi-Major Axis: 9.79 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 403

Radius: 6.8

Gravity: 8.72 G

Time & Orbit

Eccentricity (e): 0.06

Orbit Range: 9.2 AU - 10.38 AU

Year: 21144 Days

Day: 19.5 Hours

Environment

Temp: -238 °C

Axial Tilt: 38.9 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (83)

Outer Limit: 66,165,022 km

  • M1: 115,340 km (0.033 R)
  • M2: 535,860 km (0.101 R)
  • M3: 653,294 km (0.092 R)
  • M4: 1,055,712 km (0.045 R)
  • M5: 1,334,712 km (0.111 R)
  • M6: 1,780,215 km (0.099 R)
  • M7: 2,142,989 km (0.112 R)
  • M8: 2,237,236 km (0.057 R)
  • M9: 2,900,404 km (0.072 R)
  • M10: 4,433,183 km (0.071 R)
  • M11: 4,553,759 km (0.053 R)
  • M12: 5,818,609 km (0.085 R)
  • M13: 6,443,779 km (0.119 R)
  • M14: 6,580,511 km (0.051 R)
  • M15: 7,854,038 km (0.032 R)
  • M16: 8,049,113 km (0.047 R)
  • M17: 8,098,032 km (0.061 R)
  • M18: 10,191,505 km (0.088 R)
  • M19: 11,379,910 km (0.118 R)
  • M20: 11,434,962 km (0.079 R)
  • M21: 11,934,469 km (0.112 R)
  • M22: 12,158,717 km (0.11 R)
  • M23: 12,497,705 km (0.036 R)
  • M24: 13,650,207 km (0.084 R)
  • M25: 14,836,369 km (0.092 R)
  • M26: 15,198,545 km (0.064 R)
  • M27: 15,320,019 km (0.057 R)
  • M28: 15,747,420 km (0.103 R)
  • M29: 16,676,572 km (0.082 R)
  • M30: 16,801,786 km (0.109 R)
  • M31: 16,927,298 km (0.117 R)
  • M32: 17,687,106 km (0.025 R)
  • M33: 18,457,834 km (0.101 R)
  • M34: 19,833,087 km (0.097 R)
  • M35: 20,098,773 km (0.112 R)
  • M36: 20,633,586 km (0.075 R)
  • M37: 20,902,862 km (0.053 R)
  • M38: 21,105,567 km (0.091 R)
  • M39: 22,335,112 km (0.085 R)
  • M40: 22,473,191 km (0.119 R)
  • M41: 22,958,636 km (0.055 R)
  • M42: 25,077,989 km (0.07 R)
  • M43: 26,015,668 km (0.074 R)
  • M44: 26,452,195 km (0.097 R)
  • M45: 26,817,961 km (0.041 R)
  • M46: 28,222,835 km (0.088 R)
  • M47: 28,297,484 km (0.1 R)
  • M48: 30,031,473 km (0.085 R)
  • M49: 30,412,948 km (0.113 R)
  • M50: 30,565,987 km (0.085 R)
  • M51: 30,872,812 km (0.061 R)
  • M52: 31,412,262 km (0.103 R)
  • M53: 32,892,084 km (0.106 R)
  • M54: 33,285,377 km (0.074 R)
  • M55: 33,522,040 km (0.046 R)
  • M56: 37,138,719 km (0.081 R)
  • M57: 38,288,827 km (0.12 R)
  • M58: 39,450,754 km (0.081 R)
  • M59: 39,868,431 km (0.116 R)
  • M60: 40,539,976 km (0.083 R)
  • M61: 40,624,050 km (0.101 R)
  • M62: 41,130,439 km (0.094 R)
  • M63: 42,405,611 km (0.09 R)
  • M64: 43,779,966 km (0.05 R)
  • M65: 44,039,220 km (0.113 R)
  • M66: 45,168,833 km (0.064 R)
  • M67: 45,256,198 km (0.111 R)
  • M68: 45,868,802 km (0.033 R)
  • M69: 47,190,648 km (0.077 R)
  • M70: 48,525,061 km (0.11 R)
  • M71: 49,241,785 km (0.104 R)
  • M72: 50,595,197 km (0.116 R)
  • M73: 52,326,792 km (0.113 R)
  • M74: 52,510,199 km (0.075 R)
  • M75: 53,061,766 km (0.099 R)
  • M76: 53,153,919 km (0.107 R)
  • M77: 54,356,087 km (0.081 R)
  • M78: 54,448,987 km (0.118 R)
  • M79: 55,660,880 km (0.09 R)
  • M80: 55,754,378 km (0.09 R)
  • M81: 58,967,441 km (0.085 R)
  • M82: 60,500,221 km (0.081 R)
  • M83: 62,142,955 km (0.091 R)

Kuiper Belt

Range: 30 - 52 AU

Composition

Type: Dwarf Planets/TNOs (Ices)

Reservoir of dwarf planets and volatile ices.

Outer System

Oort Cloud

Range: 436 - 18,716 AU

Composition

Type: Cometary Reservoir

System's final boundary, containing trillions of icy planetesimals.

Gravitational Limit