Star System Generated (Seed: 1766920213)

Star Details

Spectral Class: K7V

Temperature: 4,021 K

Mass: 0.66 sol

Luminosity: 0.23 lux

Habitable Zone (HZ)

Inner Boundary: 0.46 AU

Outer Boundary: 0.66 AU

Physical Limits

Snow Line: 2.3 AU

Max System Radius: 16.2 AU

Planetary System (8 Planets)

Planet 1 - Terrestrial

Semi-Major Axis: 1.1 AU

Status: Outer (Cold)

Composition: Rocky (Silicates/Metals)

Physical Data

Mass: 1.51

Radius: 1.18

Gravity: 1.08 G

Time & Orbit

Eccentricity (e): 0.234

Orbit Range: 0.84 AU - 1.36 AU

Year: 519 Days

Day: 47.8 Hours

Environment

Temp: -78 °C

Axial Tilt: 36.6 °

Atmosphere: Thin Nâ‚‚/CHâ‚„

Biome: Ice Cap/Desert

Planet 2 - Terrestrial

Semi-Major Axis: 1.31 AU

Status: Outer (Cold)

Composition: Rocky (Silicates/Metals)

Physical Data

Mass: 4.59

Radius: 1.84

Gravity: 1.36 G

Time & Orbit

Eccentricity (e): 0.228

Orbit Range: 1.01 AU - 1.61 AU

Year: 674 Days

Day: 15.6 Hours

Environment

Temp: -92 °C

Axial Tilt: 10.7 °

Atmosphere: Thin Nâ‚‚/CHâ‚„

Biome: Ice Cap/Desert

Satellites (1)

Outer Limit: 57,524,007 km

  • M1: 520,301 km (0.103 R)

Planet 3 - Terrestrial

Semi-Major Axis: 1.6 AU

Status: Outer (Cold)

Composition: Rocky (Silicates/Metals)

Physical Data

Mass: 2.61

Radius: 1.47

Gravity: 1.21 G

Time & Orbit

Eccentricity (e): 0.096

Orbit Range: 1.45 AU - 1.75 AU

Year: 910 Days

Day: 41.6 Hours

Environment

Temp: -102 °C

Axial Tilt: 10.8 °

Atmosphere: Thin Nâ‚‚/CHâ‚„

Biome: Ice Cap/Desert

Planet 4 - Gas Giant

Semi-Major Axis: 2.55 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 310.3

Radius: 11.9

Gravity: 2.19 G

Time & Orbit

Eccentricity (e): 0.154

Orbit Range: 2.16 AU - 2.94 AU

Year: 1831 Days

Day: 14.1 Hours

Environment

Temp: -136 °C

Axial Tilt: 43.6 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (58)

Outer Limit: 57,524,007 km

  • M1: 159,771 km (0.086 R)
  • M2: 267,481 km (0.055 R)
  • M3: 428,299 km (0.105 R)
  • M4: 569,818 km (0.103 R)
  • M5: 653,593 km (0.07 R)
  • M6: 849,417 km (0.099 R)
  • M7: 998,715 km (0.104 R)
  • M8: 1,180,626 km (0.066 R)
  • M9: 1,357,451 km (0.096 R)
  • M10: 1,666,221 km (0.039 R)
  • M11: 1,847,534 km (0.091 R)
  • M12: 1,940,733 km (0.077 R)
  • M13: 2,016,430 km (0.117 R)
  • M14: 2,210,309 km (0.075 R)
  • M15: 2,339,711 km (0.102 R)
  • M16: 2,543,912 km (0.093 R)
  • M17: 2,658,653 km (0.032 R)
  • M18: 2,732,704 km (0.119 R)
  • M19: 2,958,896 km (0.109 R)
  • M20: 3,113,281 km (0.081 R)
  • M21: 3,191,371 km (0.069 R)
  • M22: 3,627,449 km (0.086 R)
  • M23: 3,876,530 km (0.117 R)
  • M24: 3,973,020 km (0.056 R)
  • M25: 4,131,444 km (0.076 R)
  • M26: 4,811,965 km (0.087 R)
  • M27: 4,889,906 km (0.098 R)
  • M28: 5,258,515 km (0.06 R)
  • M29: 5,432,796 km (0.109 R)
  • M30: 5,568,182 km (0.048 R)
  • M31: 6,107,034 km (0.112 R)
  • M32: 6,191,407 km (0.099 R)
  • M33: 6,332,927 km (0.117 R)
  • M34: 6,418,347 km (0.054 R)
  • M35: 6,590,385 km (0.093 R)
  • M36: 6,691,513 km (0.076 R)
  • M37: 6,778,579 km (0.116 R)
  • M38: 6,968,418 km (0.045 R)
  • M39: 7,086,302 km (0.072 R)
  • M40: 7,204,633 km (0.111 R)
  • M41: 7,323,713 km (0.082 R)
  • M42: 7,398,512 km (0.108 R)
  • M43: 7,639,514 km (0.117 R)
  • M44: 7,944,545 km (0.077 R)
  • M45: 8,067,664 km (0.088 R)
  • M46: 8,175,823 km (0.1 R)
  • M47: 8,440,761 km (0.115 R)
  • M48: 8,534,858 km (0.061 R)
  • M49: 9,027,035 km (0.09 R)
  • M50: 9,398,187 km (0.111 R)
  • M51: 9,495,874 km (0.104 R)
  • M52: 9,790,881 km (0.046 R)
  • M53: 10,255,832 km (0.113 R)
  • M54: 10,457,340 km (0.074 R)
  • M55: 10,575,522 km (0.039 R)
  • M56: 10,660,195 km (0.099 R)
  • M57: 11,397,563 km (0.117 R)
  • M58: 11,588,898 km (0.116 R)

Planet 5 - Gas Giant

Semi-Major Axis: 3.32 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 447

Radius: 14.6

Gravity: 2.1 G

Time & Orbit

Eccentricity (e): 0

Orbit Range: 3.32 AU - 3.32 AU

Year: 2720 Days

Day: 6 Hours

Environment

Temp: -166 °C

Axial Tilt: 7 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (63)

Outer Limit: 57,524,007 km

  • M1: 196,272 km (0.077 R)
  • M2: 357,539 km (0.092 R)
  • M3: 501,452 km (0.037 R)
  • M4: 785,987 km (0.051 R)
  • M5: 953,986 km (0.055 R)
  • M6: 1,125,275 km (0.053 R)
  • M7: 1,339,051 km (0.107 R)
  • M8: 1,511,537 km (0.075 R)
  • M9: 1,634,506 km (0.104 R)
  • M10: 2,123,991 km (0.083 R)
  • M11: 2,366,339 km (0.072 R)
  • M12: 2,658,653 km (0.109 R)
  • M13: 2,836,974 km (0.098 R)
  • M14: 2,962,935 km (0.085 R)
  • M15: 3,133,776 km (0.038 R)
  • M16: 3,322,569 km (0.094 R)
  • M17: 3,500,291 km (0.103 R)
  • M18: 4,037,048 km (0.086 R)
  • M19: 4,323,378 km (0.051 R)
  • M20: 4,865,820 km (0.106 R)
  • M21: 5,102,484 km (0.117 R)
  • M22: 5,308,480 km (0.086 R)
  • M23: 5,429,954 km (0.08 R)
  • M24: 5,534,822 km (0.076 R)
  • M25: 5,799,909 km (0.079 R)
  • M26: 6,214,595 km (0.118 R)
  • M27: 6,361,201 km (0.06 R)
  • M28: 6,453,353 km (0.063 R)
  • M29: 6,564,504 km (0.115 R)
  • M30: 7,245,474 km (0.07 R)
  • M31: 7,399,859 km (0.082 R)
  • M32: 7,948,883 km (0.115 R)
  • M33: 8,208,286 km (0.109 R)
  • M34: 8,430,139 km (0.053 R)
  • M35: 8,859,036 km (0.076 R)
  • M36: 9,086,575 km (0.115 R)
  • M37: 9,399,982 km (0.062 R)
  • M38: 9,653,251 km (0.091 R)
  • M39: 10,016,026 km (0.049 R)
  • M40: 10,209,905 km (0.083 R)
  • M41: 10,339,906 km (0.035 R)
  • M42: 10,843,153 km (0.072 R)
  • M43: 11,197,999 km (0.089 R)
  • M44: 11,376,918 km (0.111 R)
  • M45: 11,647,092 km (0.119 R)
  • M46: 11,760,188 km (0.067 R)
  • M47: 12,147,796 km (0.06 R)
  • M48: 12,239,649 km (0.05 R)
  • M49: 12,493,217 km (0.047 R)
  • M50: 12,632,343 km (0.068 R)
  • M51: 13,170,447 km (0.091 R)
  • M52: 13,739,966 km (0.094 R)
  • M53: 14,269,094 km (0.097 R)
  • M54: 14,487,507 km (0.06 R)
  • M55: 14,707,116 km (0.111 R)
  • M56: 15,297,878 km (0.096 R)
  • M57: 15,696,108 km (0.084 R)
  • M58: 16,224,039 km (0.116 R)
  • M59: 16,375,881 km (0.12 R)
  • M60: 16,502,889 km (0.062 R)
  • M61: 16,757,654 km (0.101 R)
  • M62: 16,911,291 km (0.108 R)
  • M63: 17,142,420 km (0.117 R)

Planet 6 - Gas Giant

Semi-Major Axis: 7.25 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 172.8

Radius: 12.8

Gravity: 1.05 G

Time & Orbit

Eccentricity (e): 0.248

Orbit Range: 5.45 AU - 9.05 AU

Year: 8777 Days

Day: 14.3 Hours

Environment

Temp: -185 °C

Axial Tilt: 20.1 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (80)

Outer Limit: 57,524,007 km

  • M1: 168,896 km (0.112 R)
  • M2: 302,636 km (0.079 R)
  • M3: 477,068 km (0.096 R)
  • M4: 606,171 km (0.09 R)
  • M5: 714,928 km (0.12 R)
  • M6: 929,452 km (0.068 R)
  • M7: 1,019,061 km (0.078 R)
  • M8: 1,166,265 km (0.034 R)
  • M9: 1,321,099 km (0.114 R)
  • M10: 1,408,464 km (0.097 R)
  • M11: 1,589,627 km (0.077 R)
  • M12: 1,843,644 km (0.082 R)
  • M13: 1,942,379 km (0.12 R)
  • M14: 2,145,533 km (0.101 R)
  • M15: 2,302,461 km (0.034 R)
  • M16: 2,463,428 km (0.1 R)
  • M17: 2,796,732 km (0.092 R)
  • M18: 2,949,472 km (0.034 R)
  • M19: 3,184,191 km (0.115 R)
  • M20: 3,425,043 km (0.093 R)
  • M21: 3,755,655 km (0.091 R)
  • M22: 3,924,850 km (0.118 R)
  • M23: 4,096,588 km (0.114 R)
  • M24: 4,315,001 km (0.027 R)
  • M25: 4,717,718 km (0.117 R)
  • M26: 4,900,677 km (0.098 R)
  • M27: 5,085,879 km (0.107 R)
  • M28: 5,203,014 km (0.055 R)
  • M29: 5,368,320 km (0.087 R)
  • M30: 5,463,613 km (0.034 R)
  • M31: 5,631,761 km (0.114 R)
  • M32: 5,899,392 km (0.111 R)
  • M33: 5,997,827 km (0.069 R)
  • M34: 6,422,237 km (0.099 R)
  • M35: 6,574,378 km (0.11 R)
  • M36: 7,221,239 km (0.109 R)
  • M37: 7,592,391 km (0.099 R)
  • M38: 7,915,523 km (0.12 R)
  • M39: 8,160,863 km (0.088 R)
  • M40: 8,243,291 km (0.055 R)
  • M41: 8,687,148 km (0.061 R)
  • M42: 9,195,931 km (0.082 R)
  • M43: 10,659,746 km (0.083 R)
  • M44: 11,052,141 km (0.048 R)
  • M45: 11,173,764 km (0.051 R)
  • M46: 11,418,506 km (0.111 R)
  • M47: 11,882,260 km (0.117 R)
  • M48: 12,069,556 km (0.058 R)
  • M49: 12,226,335 km (0.066 R)
  • M50: 12,352,296 km (0.109 R)
  • M51: 12,605,416 km (0.09 R)
  • M52: 12,988,386 km (0.112 R)
  • M53: 13,962,418 km (0.082 R)
  • M54: 14,061,153 km (0.114 R)
  • M55: 14,458,335 km (0.108 R)
  • M56: 14,558,266 km (0.083 R)
  • M57: 15,365,496 km (0.028 R)
  • M58: 15,569,698 km (0.098 R)
  • M59: 16,534,005 km (0.108 R)
  • M60: 17,023,490 km (0.067 R)
  • M61: 17,164,261 km (0.11 R)
  • M62: 17,873,804 km (0.112 R)
  • M63: 18,124,380 km (0.053 R)
  • M64: 18,376,154 km (0.081 R)
  • M65: 18,628,974 km (0.041 R)
  • M66: 19,578,621 km (0.07 R)
  • M67: 19,947,978 km (0.109 R)
  • M68: 20,394,379 km (0.077 R)
  • M69: 20,994,565 km (0.045 R)
  • M70: 23,219,086 km (0.116 R)
  • M71: 23,375,116 km (0.108 R)
  • M72: 23,806,407 km (0.048 R)
  • M73: 23,924,439 km (0.048 R)
  • M74: 24,676,767 km (0.099 R)
  • M75: 25,075,894 km (0.118 R)
  • M76: 25,396,782 km (0.032 R)
  • M77: 26,367,373 km (0.076 R)
  • M78: 26,611,965 km (0.053 R)
  • M79: 27,308,942 km (0.082 R)
  • M80: 27,638,955 km (0.064 R)

Planet 7 - Ice Giant

Semi-Major Axis: 14.15 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 125.1

Radius: 7

Gravity: 2.55 G

Time & Orbit

Eccentricity (e): 0.011

Orbit Range: 13.99 AU - 14.31 AU

Year: 23931 Days

Day: 17.8 Hours

Environment

Temp: -202 °C

Axial Tilt: 27.8 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (91)

Outer Limit: 57,524,007 km

  • M1: 391,498 km (0.066 R)
  • M2: 475,572 km (0.09 R)
  • M3: 630,106 km (0.07 R)
  • M4: 818,749 km (0.057 R)
  • M5: 1,398,441 km (0.071 R)
  • M6: 1,486,704 km (0.094 R)
  • M7: 2,796,433 km (0.098 R)
  • M8: 3,022,176 km (0.071 R)
  • M9: 3,166,239 km (0.09 R)
  • M10: 3,283,224 km (0.03 R)
  • M11: 3,431,326 km (0.057 R)
  • M12: 4,333,701 km (0.108 R)
  • M13: 4,627,960 km (0.116 R)
  • M14: 5,167,260 km (0.087 R)
  • M15: 5,761,762 km (0.081 R)
  • M16: 6,414,757 km (0.085 R)
  • M17: 6,488,808 km (0.094 R)
  • M18: 6,825,403 km (0.066 R)
  • M19: 7,437,707 km (0.105 R)
  • M20: 8,388,850 km (0.116 R)
  • M21: 8,591,855 km (0.082 R)
  • M22: 8,673,535 km (0.118 R)
  • M23: 8,755,365 km (0.103 R)
  • M24: 9,044,089 km (0.088 R)
  • M25: 9,210,442 km (0.115 R)
  • M26: 9,335,954 km (0.104 R)
  • M27: 11,062,164 km (0.087 R)
  • M28: 11,106,595 km (0.07 R)
  • M29: 11,284,766 km (0.08 R)
  • M30: 11,508,863 km (0.062 R)
  • M31: 11,734,457 km (0.119 R)
  • M32: 11,961,397 km (0.118 R)
  • M33: 12,419,914 km (0.096 R)
  • M34: 12,837,442 km (0.046 R)
  • M35: 12,930,791 km (0.105 R)
  • M36: 13,495,972 km (0.107 R)
  • M37: 13,543,544 km (0.089 R)
  • M38: 14,553,030 km (0.09 R)
  • M39: 14,993,147 km (0.084 R)
  • M40: 15,091,583 km (0.1 R)
  • M41: 15,437,603 km (0.115 R)
  • M42: 15,886,396 km (0.086 R)
  • M43: 16,440,656 km (0.071 R)
  • M44: 16,542,233 km (0.078 R)
  • M45: 16,847,862 km (0.089 R)
  • M46: 16,950,187 km (0.115 R)
  • M47: 17,413,043 km (0.072 R)
  • M48: 17,568,325 km (0.118 R)
  • M49: 18,298,812 km (0.065 R)
  • M50: 19,252,498 km (0.081 R)
  • M51: 19,359,460 km (0.102 R)
  • M52: 21,595,649 km (0.101 R)
  • M53: 21,985,501 km (0.084 R)
  • M54: 22,998,728 km (0.083 R)
  • M55: 25,597,542 km (0.091 R)
  • M56: 25,891,951 km (0.098 R)
  • M57: 26,069,224 km (0.059 R)
  • M58: 26,306,038 km (0.104 R)
  • M59: 26,424,818 km (0.057 R)
  • M60: 27,260,921 km (0.092 R)
  • M61: 27,501,325 km (0.104 R)
  • M62: 27,682,188 km (0.119 R)
  • M63: 27,863,351 km (0.103 R)
  • M64: 28,897,671 km (0.078 R)
  • M65: 30,192,740 km (0.09 R)
  • M66: 30,441,521 km (0.109 R)
  • M67: 30,691,050 km (0.118 R)
  • M68: 31,632,619 km (0.09 R)
  • M69: 32,265,568 km (0.057 R)
  • M70: 33,672,985 km (0.103 R)
  • M71: 33,801,788 km (0.079 R)
  • M72: 37,011,560 km (0.069 R)
  • M73: 37,077,982 km (0.095 R)
  • M74: 37,277,845 km (0.117 R)
  • M75: 37,344,416 km (0.052 R)
  • M76: 37,879,228 km (0.106 R)
  • M77: 38,753,628 km (0.074 R)
  • M78: 39,024,101 km (0.075 R)
  • M79: 39,498,775 km (0.068 R)
  • M80: 41,623,962 km (0.038 R)
  • M81: 41,900,868 km (0.058 R)
  • M82: 42,178,372 km (0.12 R)
  • M83: 42,386,911 km (0.05 R)
  • M84: 43,154,498 km (0.105 R)
  • M85: 44,420,395 km (0.079 R)
  • M86: 44,845,103 km (0.036 R)
  • M87: 45,342,367 km (0.105 R)
  • M88: 46,629,208 km (0.12 R)
  • M89: 46,772,821 km (0.113 R)
  • M90: 48,072,977 km (0.041 R)
  • M91: 48,581,759 km (0.071 R)

Planet 8 - Ice Giant

Semi-Major Axis: 14.19 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 205

Radius: 5.4

Gravity: 7.03 G

Time & Orbit

Eccentricity (e): 0.065

Orbit Range: 13.27 AU - 15.11 AU

Year: 24032 Days

Day: 20.8 Hours

Environment

Temp: -211 °C

Axial Tilt: 47.9 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (89)

Outer Limit: 57,524,007 km

  • M1: 81,680 km (0.117 R)
  • M2: 124,615 km (0.043 R)
  • M3: 336,296 km (0.105 R)
  • M4: 748,438 km (0.098 R)
  • M5: 1,019,360 km (0.115 R)
  • M6: 1,063,641 km (0.053 R)
  • M7: 1,131,259 km (0.115 R)
  • M8: 2,545,707 km (0.053 R)
  • M9: 2,667,629 km (0.07 R)
  • M10: 2,822,613 km (0.064 R)
  • M11: 3,044,765 km (0.111 R)
  • M12: 4,023,584 km (0.041 R)
  • M13: 4,863,277 km (0.108 R)
  • M14: 4,900,976 km (0.03 R)
  • M15: 4,938,824 km (0.097 R)
  • M16: 5,439,229 km (0.086 R)
  • M17: 5,556,963 km (0.094 R)
  • M18: 5,996,032 km (0.101 R)
  • M19: 6,949,719 km (0.108 R)
  • M20: 7,120,410 km (0.092 R)
  • M21: 7,860,919 km (0.064 R)
  • M22: 8,128,101 km (0.068 R)
  • M23: 8,353,096 km (0.11 R)
  • M24: 8,809,071 km (0.083 R)
  • M25: 9,040,199 km (0.037 R)
  • M26: 9,840,698 km (0.105 R)
  • M27: 10,860,357 km (0.08 R)
  • M28: 11,058,424 km (0.06 R)
  • M29: 12,271,513 km (0.064 R)
  • M30: 13,208,744 km (0.074 R)
  • M31: 13,473,233 km (0.088 R)
  • M32: 13,685,961 km (0.117 R)
  • M33: 13,953,592 km (0.078 R)
  • M34: 14,439,486 km (0.029 R)
  • M35: 15,096,071 km (0.073 R)
  • M36: 15,151,123 km (0.112 R)
  • M37: 16,211,772 km (0.082 R)
  • M38: 16,438,113 km (0.102 R)
  • M39: 16,608,505 km (0.075 R)
  • M40: 17,759,661 km (0.067 R)
  • M41: 18,817,467 km (0.078 R)
  • M42: 19,534,041 km (0.106 R)
  • M43: 19,835,182 km (0.119 R)
  • M44: 20,809,363 km (0.09 R)
  • M45: 21,116,936 km (0.088 R)
  • M46: 23,184,379 km (0.094 R)
  • M47: 23,503,321 km (0.071 R)
  • M48: 24,274,498 km (0.113 R)
  • M49: 24,728,079 km (0.07 R)
  • M50: 26,637,247 km (0.096 R)
  • M51: 26,770,689 km (0.1 R)
  • M52: 26,904,279 km (0.106 R)
  • M53: 27,239,379 km (0.117 R)
  • M54: 27,710,762 km (0.037 R)
  • M55: 27,981,384 km (0.118 R)
  • M56: 28,798,338 km (0.113 R)
  • M57: 29,072,401 km (0.106 R)
  • M58: 29,969,091 km (0.061 R)
  • M59: 31,860,158 km (0.096 R)
  • M60: 33,717,415 km (0.11 R)
  • M61: 36,198,646 km (0.102 R)
  • M62: 36,716,703 km (0.104 R)
  • M63: 36,790,904 km (0.03 R)
  • M64: 37,985,143 km (0.101 R)
  • M65: 38,889,163 km (0.107 R)
  • M66: 39,116,253 km (0.066 R)
  • M67: 39,647,924 km (0.113 R)
  • M68: 40,564,809 km (0.055 R)
  • M69: 41,643,260 km (0.095 R)
  • M70: 41,720,752 km (0.065 R)
  • M71: 42,809,375 km (0.083 R)
  • M72: 42,965,556 km (0.11 R)
  • M73: 43,357,203 km (0.097 R)
  • M74: 43,907,274 km (0.118 R)
  • M75: 43,985,963 km (0.099 R)
  • M76: 44,301,614 km (0.064 R)
  • M77: 45,491,815 km (0.06 R)
  • M78: 46,933,789 km (0.1 R)
  • M79: 47,498,521 km (0.084 R)
  • M80: 48,634,866 km (0.086 R)
  • M81: 49,288,310 km (0.049 R)
  • M82: 50,109,153 km (0.064 R)
  • M83: 50,191,432 km (0.112 R)
  • M84: 50,603,724 km (0.12 R)
  • M85: 50,934,335 km (0.103 R)
  • M86: 51,514,775 km (0.068 R)
  • M87: 51,597,951 km (0.109 R)
  • M88: 52,682,087 km (0.1 R)
  • M89: 57,093,579 km (0.097 R)

Kuiper Belt

Range: 30 - 60 AU

Composition

Type: Dwarf Planets/TNOs (Ices)

Reservoir of dwarf planets and volatile ices.

Outer System

Oort Cloud

Range: 286 - 11,451 AU

Composition

Type: Cometary Reservoir

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

Gravitational Limit