Star System Generated (Seed: 1767161278)

Star Details

Spectral Class: K3V

Temperature: 4,664 K

Mass: 0.72 sol

Luminosity: 0.32 lux

Habitable Zone (HZ)

Inner Boundary: 0.54 AU

Outer Boundary: 0.78 AU

Physical Limits

Snow Line: 2.72 AU

Max System Radius: 17 AU

Planetary System (6 Planets)

Planet 1 - Terrestrial

Semi-Major Axis: 2.45 AU

Status: Outer (Cold)

Composition: Rocky (Silicates/Metals)

Physical Data

Mass: 3.96

Radius: 1.73

Gravity: 1.32 G

Time & Orbit

Eccentricity (e): 0.068

Orbit Range: 2.28 AU - 2.62 AU

Year: 1651 Days

Day: 38.3 Hours

Environment

Temp: -123 °C

Axial Tilt: 19.1 °

Atmosphere: Thin Nâ‚‚/CHâ‚„

Biome: Ice Cap/Desert

Planet 2 - Gas Giant

Semi-Major Axis: 3.08 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 728.3

Radius: 13.8

Gravity: 3.82 G

Time & Orbit

Eccentricity (e): 0.183

Orbit Range: 2.52 AU - 3.64 AU

Year: 2327 Days

Day: 12.8 Hours

Environment

Temp: -140 °C

Axial Tilt: 6.9 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (68)

Outer Limit: 34,659,706 km

  • M1: 201,957 km (0.106 R)
  • M2: 352,453 km (0.12 R)
  • M3: 555,756 km (0.096 R)
  • M4: 708,496 km (0.101 R)
  • M5: 831,465 km (0.081 R)
  • M6: 1,041,052 km (0.107 R)
  • M7: 1,226,254 km (0.087 R)
  • M8: 1,411,755 km (0.092 R)
  • M9: 1,513,930 km (0.049 R)
  • M10: 1,654,403 km (0.068 R)
  • M11: 1,961,378 km (0.088 R)
  • M12: 2,128,479 km (0.078 R)
  • M13: 2,395,212 km (0.119 R)
  • M14: 3,064,812 km (0.098 R)
  • M15: 3,229,818 km (0.107 R)
  • M16: 3,321,073 km (0.044 R)
  • M17: 3,870,995 km (0.119 R)
  • M18: 4,082,675 km (0.035 R)
  • M19: 4,298,246 km (0.114 R)
  • M20: 4,585,923 km (0.08 R)
  • M21: 4,827,523 km (0.106 R)
  • M22: 5,162,323 km (0.118 R)
  • M23: 5,323,739 km (0.11 R)
  • M24: 5,432,198 km (0.09 R)
  • M25: 5,780,462 km (0.079 R)
  • M26: 6,041,959 km (0.081 R)
  • M27: 6,231,051 km (0.106 R)
  • M28: 6,364,641 km (0.109 R)
  • M29: 6,576,622 km (0.111 R)
  • M30: 6,849,638 km (0.115 R)
  • M31: 7,266,417 km (0.11 R)
  • M32: 7,386,993 km (0.025 R)
  • M33: 7,548,709 km (0.112 R)
  • M34: 7,937,962 km (0.109 R)
  • M35: 8,062,128 km (0.081 R)
  • M36: 8,249,724 km (0.109 R)
  • M37: 8,459,909 km (0.067 R)
  • M38: 8,885,665 km (0.027 R)
  • M39: 9,253,077 km (0.108 R)
  • M40: 9,340,293 km (0.11 R)
  • M41: 9,647,567 km (0.082 R)
  • M42: 9,758,120 km (0.069 R)
  • M43: 9,935,991 km (0.101 R)
  • M44: 10,047,591 km (0.047 R)
  • M45: 10,159,790 km (0.103 R)
  • M46: 10,339,906 km (0.083 R)
  • M47: 10,521,218 km (0.095 R)
  • M48: 10,680,839 km (0.108 R)
  • M49: 11,164,190 km (0.114 R)
  • M50: 11,678,358 km (0.056 R)
  • M51: 11,890,936 km (0.112 R)
  • M52: 12,176,369 km (0.067 R)
  • M53: 12,295,898 km (0.106 R)
  • M54: 12,560,387 km (0.083 R)
  • M55: 13,119,584 km (0.1 R)
  • M56: 13,687,008 km (0.089 R)
  • M57: 14,692,904 km (0.119 R)
  • M58: 14,999,281 km (0.095 R)
  • M59: 15,592,586 km (0.074 R)
  • M60: 15,696,557 km (0.093 R)
  • M61: 15,931,276 km (0.105 R)
  • M62: 16,298,838 km (0.12 R)
  • M63: 16,536,549 km (0.118 R)
  • M64: 16,775,456 km (0.041 R)
  • M65: 16,908,599 km (0.102 R)
  • M66: 17,015,411 km (0.092 R)
  • M67: 17,932,596 km (0.102 R)
  • M68: 18,369,871 km (0.102 R)

Planet 3 - Gas Giant

Semi-Major Axis: 8.64 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 746.3

Radius: 14.6

Gravity: 3.5 G

Time & Orbit

Eccentricity (e): 0.214

Orbit Range: 6.79 AU - 10.49 AU

Year: 10932 Days

Day: 12.5 Hours

Environment

Temp: -192 °C

Axial Tilt: 32.2 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (80)

Outer Limit: 34,659,706 km

  • M1: 183,257 km (0.076 R)
  • M2: 297,251 km (0.059 R)
  • M3: 400,174 km (0.047 R)
  • M4: 1,210,396 km (0.072 R)
  • M5: 1,566,439 km (0.094 R)
  • M6: 1,684,771 km (0.068 R)
  • M7: 1,880,744 km (0.055 R)
  • M8: 2,349,734 km (0.068 R)
  • M9: 2,542,266 km (0.103 R)
  • M10: 2,654,614 km (0.06 R)
  • M11: 2,768,757 km (0.116 R)
  • M12: 2,913,867 km (0.095 R)
  • M13: 3,151,279 km (0.032 R)
  • M14: 3,272,603 km (0.105 R)
  • M15: 3,551,154 km (0.062 R)
  • M16: 3,709,279 km (0.056 R)
  • M17: 4,501,250 km (0.044 R)
  • M18: 4,881,827 km (0.073 R)
  • M19: 5,345,132 km (0.107 R)
  • M20: 5,972,545 km (0.049 R)
  • M21: 6,662,341 km (0.118 R)
  • M22: 6,779,776 km (0.076 R)
  • M23: 7,539,882 km (0.106 R)
  • M24: 7,785,672 km (0.07 R)
  • M25: 8,034,004 km (0.082 R)
  • M26: 8,795,008 km (0.033 R)
  • M27: 9,402,974 km (0.111 R)
  • M28: 10,385,683 km (0.067 R)
  • M29: 10,613,520 km (0.065 R)
  • M30: 12,787,476 km (0.102 R)
  • M31: 12,885,164 km (0.103 R)
  • M32: 13,376,892 km (0.089 R)
  • M33: 14,531,189 km (0.085 R)
  • M34: 14,837,566 km (0.05 R)
  • M35: 14,991,502 km (0.103 R)
  • M36: 15,508,662 km (0.081 R)
  • M37: 15,926,788 km (0.077 R)
  • M38: 16,401,462 km (0.102 R)
  • M39: 16,613,891 km (0.093 R)
  • M40: 17,203,007 km (0.085 R)
  • M41: 17,473,031 km (0.101 R)
  • M42: 18,567,190 km (0.056 R)
  • M43: 19,178,447 km (0.06 R)
  • M44: 19,627,241 km (0.109 R)
  • M45: 19,796,436 km (0.062 R)
  • M46: 20,022,777 km (0.109 R)
  • M47: 20,136,173 km (0.103 R)
  • M48: 21,864,178 km (0.103 R)
  • M49: 22,568,634 km (0.113 R)
  • M50: 22,864,389 km (0.103 R)
  • M51: 23,220,881 km (0.065 R)
  • M52: 23,399,949 km (0.091 R)
  • M53: 24,301,725 km (0.102 R)
  • M54: 25,768,233 km (0.059 R)
  • M55: 26,263,402 km (0.079 R)
  • M56: 28,084,906 km (0.119 R)
  • M57: 29,687,697 km (0.101 R)
  • M58: 29,882,025 km (0.108 R)
  • M59: 30,011,876 km (0.071 R)
  • M60: 30,402,326 km (0.086 R)
  • M61: 31,320,109 km (0.097 R)
  • M62: 32,580,172 km (0.103 R)
  • M63: 32,847,504 km (0.052 R)
  • M64: 33,317,241 km (0.116 R)
  • M65: 34,467,050 km (0.099 R)
  • M66: 36,875,426 km (0.111 R)
  • M67: 37,713,623 km (0.091 R)
  • M68: 37,994,418 km (0.099 R)
  • M69: 38,346,273 km (0.105 R)
  • M70: 38,628,713 km (0.113 R)
  • M71: 39,053,422 km (0.111 R)
  • M72: 39,693,701 km (0.064 R)
  • M73: 42,799,801 km (0.098 R)
  • M74: 43,975,491 km (0.109 R)
  • M75: 45,758,697 km (0.062 R)
  • M76: 46,133,291 km (0.106 R)
  • M77: 47,036,263 km (0.11 R)
  • M78: 48,783,267 km (0.104 R)
  • M79: 49,242,383 km (0.079 R)
  • M80: 51,016,015 km (0.096 R)

Planet 4 - Ice Giant

Semi-Major Axis: 10.41 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 440.4

Radius: 4.1

Gravity: 26.2 G

Time & Orbit

Eccentricity (e): 0.134

Orbit Range: 9.02 AU - 11.8 AU

Year: 14458 Days

Day: 23.5 Hours

Environment

Temp: -196 °C

Axial Tilt: 14.1 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (95)

Outer Limit: 34,659,706 km

  • M1: 272,567 km (0.078 R)
  • M2: 298,597 km (0.084 R)
  • M3: 677,678 km (0.113 R)
  • M4: 714,180 km (0.114 R)
  • M5: 808,277 km (0.084 R)
  • M6: 1,050,775 km (0.116 R)
  • M7: 1,136,345 km (0.065 R)
  • M8: 1,202,168 km (0.105 R)
  • M9: 1,672,205 km (0.082 R)
  • M10: 1,849,030 km (0.12 R)
  • M11: 1,900,641 km (0.077 R)
  • M12: 1,952,701 km (0.042 R)
  • M13: 2,005,210 km (0.118 R)
  • M14: 2,058,317 km (0.047 R)
  • M15: 2,138,801 km (0.104 R)
  • M16: 2,165,878 km (0.105 R)
  • M17: 2,192,955 km (0.097 R)
  • M18: 2,220,332 km (0.063 R)
  • M19: 2,302,910 km (0.102 R)
  • M20: 2,330,585 km (0.102 R)
  • M21: 2,556,628 km (0.111 R)
  • M22: 3,755,056 km (0.106 R)
  • M23: 3,919,614 km (0.102 R)
  • M24: 5,136,443 km (0.04 R)
  • M25: 5,429,804 km (0.111 R)
  • M26: 6,071,130 km (0.109 R)
  • M27: 6,815,679 km (0.11 R)
  • M28: 7,630,239 km (0.117 R)
  • M29: 7,671,828 km (0.079 R)
  • M30: 8,821,188 km (0.096 R)
  • M31: 9,216,126 km (0.069 R)
  • M32: 9,304,688 km (0.098 R)
  • M33: 9,393,549 km (0.109 R)
  • M34: 10,527,501 km (0.102 R)
  • M35: 10,852,727 km (0.109 R)
  • M36: 11,040,024 km (0.1 R)
  • M37: 11,370,485 km (0.076 R)
  • M38: 11,944,343 km (0.091 R)
  • M39: 12,234,712 km (0.106 R)
  • M40: 12,429,638 km (0.104 R)
  • M41: 12,822,632 km (0.041 R)
  • M42: 13,020,699 km (0.116 R)
  • M43: 13,469,942 km (0.068 R)
  • M44: 14,332,224 km (0.118 R)
  • M45: 14,537,622 km (0.089 R)
  • M46: 15,107,739 km (0.099 R)
  • M47: 15,737,995 km (0.062 R)
  • M48: 15,790,953 km (0.068 R)
  • M49: 16,162,853 km (0.099 R)
  • M50: 16,645,456 km (0.08 R)
  • M51: 17,024,088 km (0.115 R)
  • M52: 18,121,239 km (0.051 R)
  • M53: 18,232,240 km (0.115 R)
  • M54: 18,622,392 km (0.106 R)
  • M55: 19,128,033 km (0.11 R)
  • M56: 19,354,225 km (0.093 R)
  • M57: 19,524,467 km (0.11 R)
  • M58: 21,429,745 km (0.097 R)
  • M59: 22,374,456 km (0.08 R)
  • M60: 22,851,972 km (0.107 R)
  • M61: 25,413,387 km (0.106 R)
  • M62: 26,727,754 km (0.102 R)
  • M63: 26,790,884 km (0.098 R)
  • M64: 28,064,112 km (0.106 R)
  • M65: 28,643,504 km (0.118 R)
  • M66: 29,552,611 km (0.088 R)
  • M67: 31,732,401 km (0.038 R)
  • M68: 32,470,517 km (0.117 R)
  • M69: 33,214,168 km (0.105 R)
  • M70: 33,554,054 km (0.098 R)
  • M71: 33,826,771 km (0.09 R)
  • M72: 34,237,268 km (0.083 R)
  • M73: 34,305,933 km (0.118 R)
  • M74: 35,063,347 km (0.083 R)
  • M75: 36,384,446 km (0.088 R)
  • M76: 36,524,470 km (0.093 R)
  • M77: 36,664,643 km (0.077 R)
  • M78: 37,227,131 km (0.101 R)
  • M79: 38,360,784 km (0.116 R)
  • M80: 40,952,716 km (0.091 R)
  • M81: 41,025,570 km (0.084 R)
  • M82: 41,536,298 km (0.099 R)
  • M83: 43,674,799 km (0.055 R)
  • M84: 43,972,649 km (0.11 R)
  • M85: 44,196,447 km (0.068 R)
  • M86: 46,000,148 km (0.088 R)
  • M87: 46,075,845 km (0.041 R)
  • M88: 46,530,772 km (0.083 R)
  • M89: 46,834,905 km (0.106 R)
  • M90: 49,523,926 km (0.089 R)
  • M91: 50,223,446 km (0.031 R)
  • M92: 50,301,386 km (0.112 R)
  • M93: 51,082,886 km (0.064 R)
  • M94: 51,789,736 km (0.094 R)
  • M95: 51,947,262 km (0.07 R)

Planet 5 - Ice Giant

Semi-Major Axis: 13.33 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 685.2

Radius: 6.5

Gravity: 16.22 G

Time & Orbit

Eccentricity (e): 0.06

Orbit Range: 12.53 AU - 14.13 AU

Year: 20949 Days

Day: 19 Hours

Environment

Temp: -200 °C

Axial Tilt: 26.8 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (97)

Outer Limit: 34,659,706 km

  • M1: 171,290 km (0.069 R)
  • M2: 286,181 km (0.088 R)
  • M3: 780,003 km (0.114 R)
  • M4: 854,353 km (0.114 R)
  • M5: 1,175,989 km (0.112 R)
  • M6: 1,564,195 km (0.056 R)
  • M7: 1,627,176 km (0.106 R)
  • M8: 2,376,661 km (0.05 R)
  • M9: 2,825,006 km (0.049 R)
  • M10: 2,980,289 km (0.095 R)
  • M11: 3,504,330 km (0.091 R)
  • M12: 4,635,739 km (0.03 R)
  • M13: 6,370,326 km (0.088 R)
  • M14: 7,093,482 km (0.063 R)
  • M15: 7,897,122 km (0.092 R)
  • M16: 8,061,231 km (0.072 R)
  • M17: 8,281,888 km (0.053 R)
  • M18: 8,560,589 km (0.03 R)
  • M19: 8,672,787 km (0.098 R)
  • M20: 8,729,185 km (0.111 R)
  • M21: 9,012,673 km (0.116 R)
  • M22: 9,822,596 km (0.073 R)
  • M23: 9,881,388 km (0.065 R)
  • M24: 10,415,303 km (0.06 R)
  • M25: 10,655,707 km (0.097 R)
  • M26: 11,203,085 km (0.117 R)
  • M27: 11,511,257 km (0.052 R)
  • M28: 11,573,190 km (0.061 R)
  • M29: 11,697,357 km (0.117 R)
  • M30: 13,157,731 km (0.117 R)
  • M31: 13,876,250 km (0.079 R)
  • M32: 14,008,345 km (0.098 R)
  • M33: 14,074,467 km (0.095 R)
  • M34: 14,207,160 km (0.03 R)
  • M35: 14,473,594 km (0.038 R)
  • M36: 14,540,464 km (0.096 R)
  • M37: 14,674,654 km (0.119 R)
  • M38: 15,079,316 km (0.12 R)
  • M39: 19,990,165 km (0.109 R)
  • M40: 20,739,501 km (0.067 R)
  • M41: 20,966,142 km (0.106 R)
  • M42: 23,120,351 km (0.067 R)
  • M43: 24,303,072 km (0.119 R)
  • M44: 26,727,006 km (0.077 R)
  • M45: 27,220,978 km (0.106 R)
  • M46: 27,717,942 km (0.092 R)
  • M47: 27,884,146 km (0.06 R)
  • M48: 29,057,741 km (0.092 R)
  • M49: 29,142,114 km (0.11 R)
  • M50: 29,226,637 km (0.119 R)
  • M51: 30,675,941 km (0.056 R)
  • M52: 33,113,638 km (0.105 R)
  • M53: 33,910,247 km (0.069 R)
  • M54: 34,444,910 km (0.105 R)
  • M55: 34,802,897 km (0.057 R)
  • M56: 35,251,990 km (0.056 R)
  • M57: 38,542,395 km (0.11 R)
  • M58: 38,913,997 km (0.04 R)
  • M59: 39,473,642 km (0.081 R)
  • M60: 40,223,875 km (0.113 R)
  • M61: 43,079,400 km (0.068 R)
  • M62: 44,823,711 km (0.111 R)
  • M63: 45,508,271 km (0.109 R)
  • M64: 46,986,896 km (0.032 R)
  • M65: 47,185,113 km (0.096 R)
  • M66: 48,380,999 km (0.085 R)
  • M67: 48,481,080 km (0.037 R)
  • M68: 49,485,928 km (0.114 R)
  • M69: 49,889,843 km (0.116 R)
  • M70: 49,990,971 km (0.089 R)
  • M71: 50,497,659 km (0.067 R)
  • M72: 50,700,813 km (0.076 R)
  • M73: 51,516,121 km (0.053 R)
  • M74: 52,027,895 km (0.107 R)
  • M75: 53,056,530 km (0.064 R)
  • M76: 53,884,255 km (0.116 R)
  • M77: 54,612,049 km (0.077 R)
  • M78: 54,716,319 km (0.106 R)
  • M79: 54,925,008 km (0.112 R)
  • M80: 56,709,262 km (0.047 R)
  • M81: 59,153,541 km (0.089 R)
  • M82: 61,306,703 km (0.114 R)
  • M83: 61,631,929 km (0.05 R)
  • M84: 61,740,388 km (0.088 R)
  • M85: 61,848,996 km (0.107 R)
  • M86: 62,066,361 km (0.116 R)
  • M87: 63,266,435 km (0.119 R)
  • M88: 63,375,941 km (0.095 R)
  • M89: 64,804,750 km (0.057 R)
  • M90: 67,023,736 km (0.026 R)
  • M91: 67,358,835 km (0.071 R)
  • M92: 73,483,072 km (0.113 R)
  • M93: 74,752,261 km (0.077 R)
  • M94: 76,961,373 km (0.076 R)
  • M95: 77,078,358 km (0.067 R)
  • M96: 77,312,180 km (0.087 R)
  • M97: 78,250,308 km (0.104 R)

Planet 6 - Ice Giant

Semi-Major Axis: 14.35 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 47.3

Radius: 6.2

Gravity: 1.23 G

Time & Orbit

Eccentricity (e): 0.145

Orbit Range: 12.27 AU - 16.43 AU

Year: 23399 Days

Day: 22.4 Hours

Environment

Temp: -203 °C

Axial Tilt: 19.3 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (65)

Outer Limit: 34,659,706 km

  • M1: 78,240 km (0.091 R)
  • M2: 239,207 km (0.058 R)
  • M3: 385,514 km (0.112 R)
  • M4: 636,988 km (0.101 R)
  • M5: 690,394 km (0.081 R)
  • M6: 874,400 km (0.067 R)
  • M7: 1,373,308 km (0.117 R)
  • M8: 1,735,634 km (0.119 R)
  • M9: 2,006,407 km (0.029 R)
  • M10: 2,806,606 km (0.09 R)
  • M11: 2,851,186 km (0.108 R)
  • M12: 3,193,466 km (0.055 R)
  • M13: 3,524,675 km (0.03 R)
  • M14: 3,966,588 km (0.11 R)
  • M15: 4,092,399 km (0.025 R)
  • M16: 4,504,093 km (0.097 R)
  • M17: 4,714,876 km (0.118 R)
  • M18: 5,200,920 km (0.088 R)
  • M19: 5,988,403 km (0.074 R)
  • M20: 6,993,700 km (0.097 R)
  • M21: 7,299,329 km (0.112 R)
  • M22: 7,609,296 km (0.056 R)
  • M23: 8,891,649 km (0.072 R)
  • M24: 10,273,933 km (0.062 R)
  • M25: 10,481,724 km (0.085 R)
  • M26: 10,831,335 km (0.108 R)
  • M27: 11,149,081 km (0.114 R)
  • M28: 11,326,952 km (0.094 R)
  • M29: 11,757,794 km (0.113 R)
  • M30: 11,866,402 km (0.092 R)
  • M31: 12,487,832 km (0.095 R)
  • M32: 12,561,584 km (0.098 R)
  • M33: 12,820,986 km (0.081 R)
  • M34: 13,685,812 km (0.117 R)
  • M35: 13,876,399 km (0.085 R)
  • M36: 15,194,955 km (0.057 R)
  • M37: 15,392,275 km (0.097 R)
  • M38: 15,471,412 km (0.097 R)
  • M39: 15,949,227 km (0.054 R)
  • M40: 18,158,190 km (0.082 R)
  • M41: 18,200,077 km (0.077 R)
  • M42: 19,298,125 km (0.114 R)
  • M43: 20,941,458 km (0.101 R)
  • M44: 21,558,100 km (0.08 R)
  • M45: 21,868,666 km (0.116 R)
  • M46: 23,489,110 km (0.095 R)
  • M47: 23,900,205 km (0.099 R)
  • M48: 23,946,131 km (0.083 R)
  • M49: 24,683,349 km (0.06 R)
  • M50: 25,054,801 km (0.11 R)
  • M51: 25,241,200 km (0.097 R)
  • M52: 25,428,048 km (0.07 R)
  • M53: 25,521,546 km (0.106 R)
  • M54: 25,803,090 km (0.081 R)
  • M55: 25,850,063 km (0.098 R)
  • M56: 25,991,284 km (0.116 R)
  • M57: 26,038,557 km (0.057 R)
  • M58: 26,796,419 km (0.11 R)
  • M59: 26,843,992 km (0.112 R)
  • M60: 27,946,977 km (0.117 R)
  • M61: 29,113,541 km (0.069 R)
  • M62: 29,456,718 km (0.118 R)
  • M63: 29,505,936 km (0.082 R)
  • M64: 33,013,109 km (0.106 R)
  • M65: 33,217,459 km (0.116 R)

Kuiper Belt

Range: 30 - 45 AU

Composition

Type: Dwarf Planets/TNOs (Ices)

Reservoir of dwarf planets and volatile ices.

Outer System

Oort Cloud

Range: 161 - 13,013 AU

Composition

Type: Cometary Reservoir

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

Gravitational Limit