Star System Generated (Seed: 1766910923)

Star Details

Spectral Class: M3V

Temperature: 3,267 K

Mass: 0.31 sol

Luminosity: 0.02 lux

Habitable Zone (HZ)

Inner Boundary: 0.13 AU

Outer Boundary: 0.19 AU

Physical Limits

Snow Line: 0.68 AU

Max System Radius: 11.1 AU

Planetary System (7 Planets)

Planet 1 - Terrestrial

Semi-Major Axis: 0.63 AU

Status: Outer (Cold)

Composition: Rocky (Silicates/Metals)

Physical Data

Mass: 2.83

Radius: 1.52

Gravity: 1.22 G

Time & Orbit

Eccentricity (e): 0.063

Orbit Range: 0.59 AU - 0.67 AU

Year: 328 Days

Day: 47.6 Hours

Environment

Temp: -128 °C

Axial Tilt: 1.7 °

Atmosphere: Thin Nâ‚‚/CHâ‚„

Biome: Ice Cap/Desert

Satellites (1)

Outer Limit: 81,856,514 km

  • M1: 274,063 km (0.078 R)

Planet 2 - Gas Giant

Semi-Major Axis: 1.4 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 822.2

Radius: 10.4

Gravity: 7.6 G

Time & Orbit

Eccentricity (e): 0.197

Orbit Range: 1.12 AU - 1.68 AU

Year: 1087 Days

Day: 11 Hours

Environment

Temp: -178 °C

Axial Tilt: 4.4 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (58)

Outer Limit: 81,856,514 km

  • M1: 183,108 km (0.038 R)
  • M2: 319,391 km (0.101 R)
  • M3: 393,742 km (0.109 R)
  • M4: 600,187 km (0.118 R)
  • M5: 673,190 km (0.063 R)
  • M6: 849,716 km (0.107 R)
  • M7: 961,914 km (0.098 R)
  • M8: 1,217,427 km (0.119 R)
  • M9: 1,361,789 km (0.113 R)
  • M10: 1,623,885 km (0.063 R)
  • M11: 1,729,651 km (0.113 R)
  • M12: 1,865,485 km (0.089 R)
  • M13: 2,004,761 km (0.066 R)
  • M14: 2,138,053 km (0.114 R)
  • M15: 2,504,568 km (0.109 R)
  • M16: 2,586,398 km (0.104 R)
  • M17: 2,679,597 km (0.084 R)
  • M18: 2,890,979 km (0.115 R)
  • M19: 3,118,667 km (0.119 R)
  • M20: 3,307,459 km (0.072 R)
  • M21: 3,442,995 km (0.038 R)
  • M22: 3,754,907 km (0.076 R)
  • M23: 3,860,822 km (0.101 R)
  • M24: 4,172,733 km (0.098 R)
  • M25: 4,381,123 km (0.073 R)
  • M26: 4,630,652 km (0.095 R)
  • M27: 4,744,496 km (0.117 R)
  • M28: 4,846,522 km (0.107 R)
  • M29: 5,026,788 km (0.074 R)
  • M30: 5,288,135 km (0.038 R)
  • M31: 5,460,472 km (0.085 R)
  • M32: 5,688,609 km (0.112 R)
  • M33: 5,851,670 km (0.116 R)
  • M34: 5,974,939 km (0.116 R)
  • M35: 6,237,932 km (0.077 R)
  • M36: 6,392,018 km (0.11 R)
  • M37: 6,575,724 km (0.09 R)
  • M38: 6,646,783 km (0.082 R)
  • M39: 7,020,778 km (0.113 R)
  • M40: 7,181,147 km (0.094 R)
  • M41: 7,579,825 km (0.064 R)
  • M42: 7,894,878 km (0.098 R)
  • M43: 8,092,198 km (0.075 R)
  • M44: 8,321,830 km (0.078 R)
  • M45: 8,414,282 km (0.092 R)
  • M46: 8,507,033 km (0.118 R)
  • M47: 8,662,465 km (0.119 R)
  • M48: 8,865,918 km (0.09 R)
  • M49: 9,118,589 km (0.075 R)
  • M50: 9,890,663 km (0.078 R)
  • M51: 9,972,344 km (0.077 R)
  • M52: 10,533,336 km (0.082 R)
  • M53: 10,633,566 km (0.095 R)
  • M54: 10,717,191 km (0.059 R)
  • M55: 11,053,936 km (0.109 R)
  • M56: 11,342,959 km (0.035 R)
  • M57: 11,479,841 km (0.043 R)
  • M58: 11,582,914 km (0.099 R)

Planet 3 - Gas Giant

Semi-Major Axis: 1.88 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 565.4

Radius: 14.2

Gravity: 2.8 G

Time & Orbit

Eccentricity (e): 0.219

Orbit Range: 1.47 AU - 2.29 AU

Year: 1691 Days

Day: 13.1 Hours

Environment

Temp: -197 °C

Axial Tilt: 3.7 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (60)

Outer Limit: 81,856,514 km

  • M1: 188,194 km (0.071 R)
  • M2: 281,094 km (0.071 R)
  • M3: 391,198 km (0.099 R)
  • M4: 483,650 km (0.115 R)
  • M5: 864,825 km (0.065 R)
  • M6: 957,277 km (0.09 R)
  • M7: 1,061,546 km (0.027 R)
  • M8: 1,336,358 km (0.113 R)
  • M9: 1,454,839 km (0.093 R)
  • M10: 1,654,253 km (0.103 R)
  • M11: 1,873,265 km (0.06 R)
  • M12: 2,007,304 km (0.098 R)
  • M13: 2,102,000 km (0.095 R)
  • M14: 2,198,341 km (0.12 R)
  • M15: 2,406,880 km (0.108 R)
  • M16: 2,587,594 km (0.111 R)
  • M17: 3,144,996 km (0.102 R)
  • M18: 3,418,910 km (0.092 R)
  • M19: 3,558,933 km (0.103 R)
  • M20: 3,870,995 km (0.101 R)
  • M21: 4,260,248 km (0.107 R)
  • M22: 4,536,107 km (0.059 R)
  • M23: 4,676,280 km (0.111 R)
  • M24: 4,817,799 km (0.084 R)
  • M25: 5,310,276 km (0.119 R)
  • M26: 5,788,540 km (0.102 R)
  • M27: 6,218,484 km (0.036 R)
  • M28: 6,374,664 km (0.089 R)
  • M29: 6,516,334 km (0.027 R)
  • M30: 6,674,907 km (0.086 R)
  • M31: 6,882,998 km (0.092 R)
  • M32: 6,995,944 km (0.107 R)
  • M33: 7,142,251 km (0.104 R)
  • M34: 7,240,238 km (0.099 R)
  • M35: 7,503,829 km (0.081 R)
  • M36: 7,686,937 km (0.086 R)
  • M37: 8,313,752 km (0.105 R)
  • M38: 8,416,975 km (0.064 R)
  • M39: 8,711,832 km (0.035 R)
  • M40: 8,834,203 km (0.098 R)
  • M41: 9,098,393 km (0.079 R)
  • M42: 9,401,029 km (0.115 R)
  • M43: 9,797,613 km (0.063 R)
  • M44: 10,052,977 km (0.119 R)
  • M45: 10,700,736 km (0.059 R)
  • M46: 10,944,730 km (0.057 R)
  • M47: 11,039,126 km (0.115 R)
  • M48: 11,228,667 km (0.069 R)
  • M49: 11,342,959 km (0.059 R)
  • M50: 11,438,552 km (0.095 R)
  • M51: 11,553,444 km (0.107 R)
  • M52: 12,095,137 km (0.068 R)
  • M53: 12,271,065 km (0.083 R)
  • M54: 12,408,545 km (0.062 R)
  • M55: 12,566,221 km (0.036 R)
  • M56: 12,684,852 km (0.106 R)
  • M57: 12,823,829 km (0.105 R)
  • M58: 13,083,231 km (0.035 R)
  • M59: 13,404,867 km (0.098 R)
  • M60: 13,607,273 km (0.107 R)

Planet 4 - Gas Giant

Semi-Major Axis: 2.09 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 166.5

Radius: 14.6

Gravity: 0.78 G

Time & Orbit

Eccentricity (e): 0.028

Orbit Range: 2.03 AU - 2.15 AU

Year: 1982 Days

Day: 6.6 Hours

Environment

Temp: -193 °C

Axial Tilt: 158.3 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (51)

Outer Limit: 81,856,514 km

  • M1: 190,139 km (0.12 R)
  • M2: 289,921 km (0.08 R)
  • M3: 420,370 km (0.073 R)
  • M4: 612,454 km (0.105 R)
  • M5: 906,563 km (0.092 R)
  • M6: 1,156,541 km (0.118 R)
  • M7: 1,385,426 km (0.091 R)
  • M8: 1,629,719 km (0.055 R)
  • M9: 2,083,599 km (0.052 R)
  • M10: 2,321,011 km (0.076 R)
  • M11: 2,429,469 km (0.025 R)
  • M12: 2,558,273 km (0.091 R)
  • M13: 2,784,465 km (0.034 R)
  • M14: 2,880,806 km (0.112 R)
  • M15: 3,116,572 km (0.119 R)
  • M16: 3,216,653 km (0.118 R)
  • M17: 3,420,406 km (0.073 R)
  • M18: 3,670,533 km (0.079 R)
  • M19: 4,013,561 km (0.075 R)
  • M20: 4,144,908 km (0.12 R)
  • M21: 4,277,751 km (0.083 R)
  • M22: 4,378,281 km (0.111 R)
  • M23: 4,479,708 km (0.094 R)
  • M24: 4,570,514 km (0.06 R)
  • M25: 4,846,672 km (0.115 R)
  • M26: 4,975,176 km (0.079 R)
  • M27: 5,140,332 km (0.108 R)
  • M28: 5,331,369 km (0.063 R)
  • M29: 5,549,034 km (0.112 R)
  • M30: 5,695,939 km (0.091 R)
  • M31: 5,831,624 km (0.09 R)
  • M32: 6,056,171 km (0.099 R)
  • M33: 6,232,696 km (0.113 R)
  • M34: 6,423,882 km (0.075 R)
  • M35: 6,681,789 km (0.074 R)
  • M36: 6,851,283 km (0.095 R)
  • M37: 7,128,189 km (0.082 R)
  • M38: 7,301,423 km (0.057 R)
  • M39: 7,476,154 km (0.081 R)
  • M40: 7,788,664 km (0.056 R)
  • M41: 7,981,046 km (0.075 R)
  • M42: 8,133,187 km (0.095 R)
  • M43: 8,286,525 km (0.07 R)
  • M44: 8,440,611 km (0.09 R)
  • M45: 8,680,865 km (0.049 R)
  • M46: 9,052,616 km (0.074 R)
  • M47: 9,153,744 km (0.06 R)
  • M48: 9,284,044 km (0.066 R)
  • M49: 9,502,906 km (0.075 R)
  • M50: 9,856,405 km (0.067 R)
  • M51: 9,960,376 km (0.089 R)

Planet 5 - Gas Giant

Semi-Major Axis: 5.16 AU

Status: Outer (Cold)

Composition: Hydrogen/Helium Atmosphere

Physical Data

Mass: 389.1

Radius: 10.4

Gravity: 3.6 G

Time & Orbit

Eccentricity (e): 0.042

Orbit Range: 4.94 AU - 5.38 AU

Year: 7689 Days

Day: 6.2 Hours

Environment

Temp: -207 °C

Axial Tilt: 144.4 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (81)

Outer Limit: 81,856,514 km

  • M1: 130,449 km (0.106 R)
  • M2: 404,812 km (0.033 R)
  • M3: 489,335 km (0.073 R)
  • M4: 557,402 km (0.103 R)
  • M5: 995,723 km (0.086 R)
  • M6: 1,070,672 km (0.097 R)
  • M7: 1,194,689 km (0.12 R)
  • M8: 2,313,381 km (0.078 R)
  • M9: 2,455,649 km (0.037 R)
  • M10: 2,579,815 km (0.08 R)
  • M11: 2,706,225 km (0.114 R)
  • M12: 2,813,188 km (0.119 R)
  • M13: 2,943,338 km (0.049 R)
  • M14: 3,142,453 km (0.095 R)
  • M15: 3,507,472 km (0.101 R)
  • M16: 3,600,821 km (0.102 R)
  • M17: 3,814,147 km (0.095 R)
  • M18: 3,982,894 km (0.1 R)
  • M19: 4,277,901 km (0.113 R)
  • M20: 4,580,238 km (0.066 R)
  • M21: 4,915,487 km (0.092 R)
  • M22: 5,366,076 km (0.102 R)
  • M23: 6,506,909 km (0.093 R)
  • M24: 7,178,903 km (0.08 R)
  • M25: 7,750,815 km (0.033 R)
  • M26: 8,556,998 km (0.108 R)
  • M27: 8,874,146 km (0.114 R)
  • M28: 9,130,706 km (0.09 R)
  • M29: 9,520,259 km (0.04 R)
  • M30: 9,881,987 km (0.087 R)
  • M31: 10,014,680 km (0.055 R)
  • M32: 10,181,332 km (0.067 R)
  • M33: 10,349,031 km (0.093 R)
  • M34: 10,416,350 km (0.114 R)
  • M35: 10,891,623 km (0.111 R)
  • M36: 12,039,786 km (0.096 R)
  • M37: 12,181,605 km (0.081 R)
  • M38: 12,323,873 km (0.119 R)
  • M39: 12,395,231 km (0.082 R)
  • M40: 12,790,319 km (0.113 R)
  • M41: 13,116,741 km (0.116 R)
  • M42: 13,445,857 km (0.115 R)
  • M43: 13,703,614 km (0.099 R)
  • M44: 14,336,712 km (0.08 R)
  • M45: 14,449,359 km (0.095 R)
  • M46: 14,789,245 km (0.089 R)
  • M47: 15,592,586 km (0.08 R)
  • M48: 15,824,762 km (0.048 R)
  • M49: 16,370,944 km (0.074 R)
  • M50: 16,962,903 km (0.1 R)
  • M51: 17,521,800 km (0.116 R)
  • M52: 17,642,376 km (0.111 R)
  • M53: 19,691,867 km (0.058 R)
  • M54: 20,110,741 km (0.061 R)
  • M55: 20,363,412 km (0.052 R)
  • M56: 20,659,616 km (0.113 R)
  • M57: 20,872,045 km (0.11 R)
  • M58: 21,170,791 km (0.119 R)
  • M59: 21,729,240 km (0.074 R)
  • M60: 21,902,026 km (0.045 R)
  • M61: 22,336,009 km (0.097 R)
  • M62: 22,860,499 km (0.1 R)
  • M63: 23,433,310 km (0.076 R)
  • M64: 23,788,305 km (0.076 R)
  • M65: 24,055,637 km (0.071 R)
  • M66: 24,368,745 km (0.106 R)
  • M67: 25,089,508 km (0.062 R)
  • M68: 25,361,776 km (0.101 R)
  • M69: 25,954,632 km (0.117 R)
  • M70: 26,459,974 km (0.11 R)
  • M71: 27,014,982 km (0.09 R)
  • M72: 27,573,730 km (0.063 R)
  • M73: 27,760,877 km (0.1 R)
  • M74: 28,183,491 km (0.113 R)
  • M75: 28,560,926 km (0.05 R)
  • M76: 28,940,007 km (0.115 R)
  • M77: 29,177,718 km (0.073 R)
  • M78: 29,991,082 km (0.044 R)
  • M79: 31,346,738 km (0.071 R)
  • M80: 31,591,031 km (0.043 R)
  • M81: 31,688,868 km (0.099 R)

Planet 6 - Ice Giant

Semi-Major Axis: 8.14 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 98.1

Radius: 3

Gravity: 10.9 G

Time & Orbit

Eccentricity (e): 0.148

Orbit Range: 6.94 AU - 9.34 AU

Year: 15235 Days

Day: 17.7 Hours

Environment

Temp: -228 °C

Axial Tilt: 29.7 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (48)

Outer Limit: 81,856,514 km

  • M1: 42,785 km (0.059 R)
  • M2: 92,302 km (0.108 R)
  • M3: 117,434 km (0.078 R)
  • M4: 302,636 km (0.068 R)
  • M5: 476,768 km (0.096 R)
  • M6: 917,933 km (0.076 R)
  • M7: 1,101,938 km (0.062 R)
  • M8: 2,041,712 km (0.097 R)
  • M9: 2,120,251 km (0.064 R)
  • M10: 2,805,858 km (0.105 R)
  • M11: 2,827,699 km (0.099 R)
  • M12: 2,915,214 km (0.072 R)
  • M13: 4,233,021 km (0.044 R)
  • M14: 4,664,611 km (0.077 R)
  • M15: 5,243,705 km (0.118 R)
  • M16: 5,514,477 km (0.118 R)
  • M17: 6,125,734 km (0.069 R)
  • M18: 7,411,228 km (0.117 R)
  • M19: 7,775,948 km (0.084 R)
  • M20: 7,806,466 km (0.116 R)
  • M21: 9,000,556 km (0.099 R)
  • M22: 9,585,783 km (0.06 R)
  • M23: 10,283,806 km (0.113 R)
  • M24: 11,378,713 km (0.11 R)
  • M25: 13,973,638 km (0.112 R)
  • M26: 14,687,519 km (0.104 R)
  • M27: 15,722,287 km (0.1 R)
  • M28: 15,955,510 km (0.076 R)
  • M29: 16,346,559 km (0.114 R)
  • M30: 19,712,063 km (0.07 R)
  • M31: 19,753,800 km (0.048 R)
  • M32: 21,193,082 km (0.097 R)
  • M33: 22,055,364 km (0.117 R)
  • M34: 23,547,303 km (0.072 R)
  • M35: 23,591,734 km (0.115 R)
  • M36: 25,252,869 km (0.091 R)
  • M37: 25,982,906 km (0.111 R)
  • M38: 26,350,468 km (0.117 R)
  • M39: 26,488,697 km (0.082 R)
  • M40: 26,627,374 km (0.086 R)
  • M41: 26,766,051 km (0.082 R)
  • M42: 26,812,426 km (0.105 R)
  • M43: 27,230,403 km (0.105 R)
  • M44: 27,370,127 km (0.092 R)
  • M45: 27,510,300 km (0.101 R)
  • M46: 28,876,279 km (0.071 R)
  • M47: 31,039,314 km (0.081 R)
  • M48: 32,905,996 km (0.081 R)

Planet 7 - Ice Giant

Semi-Major Axis: 9.51 AU

Status: Outer (Cold)

Composition: Methane/Ammonia Ices

Physical Data

Mass: 921.7

Radius: 3.3

Gravity: 84.64 G

Time & Orbit

Eccentricity (e): 0.186

Orbit Range: 7.74 AU - 11.28 AU

Year: 19239 Days

Day: 16.8 Hours

Environment

Temp: -232 °C

Axial Tilt: 28.1 °

Atmosphere: Hâ‚‚, CHâ‚„

Biome: None

Satellites (94)

Outer Limit: 81,856,514 km

  • M1: 79,137 km (0.087 R)
  • M2: 695,630 km (0.099 R)
  • M3: 745,297 km (0.094 R)
  • M4: 874,699 km (0.092 R)
  • M5: 901,477 km (0.077 R)
  • M6: 928,404 km (0.085 R)
  • M7: 1,011,132 km (0.103 R)
  • M8: 1,183,918 km (0.071 R)
  • M9: 1,997,431 km (0.095 R)
  • M10: 2,706,225 km (0.061 R)
  • M11: 3,484,583 km (0.117 R)
  • M12: 3,700,303 km (0.056 R)
  • M13: 4,511,722 km (0.086 R)
  • M14: 4,841,735 km (0.088 R)
  • M15: 4,985,499 km (0.065 R)
  • M16: 5,130,609 km (0.036 R)
  • M17: 5,725,260 km (0.115 R)
  • M18: 6,393,514 km (0.091 R)
  • M19: 6,551,190 km (0.068 R)
  • M20: 6,816,876 km (0.119 R)
  • M21: 7,140,456 km (0.064 R)
  • M22: 7,970,724 km (0.097 R)
  • M23: 8,083,820 km (0.074 R)
  • M24: 8,714,824 km (0.042 R)
  • M25: 10,206,614 km (0.059 R)
  • M26: 10,638,353 km (0.067 R)
  • M27: 10,700,436 km (0.084 R)
  • M28: 11,583,214 km (0.114 R)
  • M29: 11,839,774 km (0.093 R)
  • M30: 12,227,980 km (0.106 R)
  • M31: 14,712,651 km (0.079 R)
  • M32: 14,920,742 km (0.104 R)
  • M33: 16,476,261 km (0.068 R)
  • M34: 17,054,606 km (0.119 R)
  • M35: 18,231,044 km (0.09 R)
  • M36: 19,814,537 km (0.104 R)
  • M37: 20,583,919 km (0.117 R)
  • M38: 21,756,018 km (0.106 R)
  • M39: 22,549,485 km (0.1 R)
  • M40: 22,629,371 km (0.041 R)
  • M41: 24,820,980 km (0.103 R)
  • M42: 25,068,714 km (0.111 R)
  • M43: 25,317,196 km (0.113 R)
  • M44: 25,400,073 km (0.106 R)
  • M45: 27,760,877 km (0.09 R)
  • M46: 29,054,001 km (0.056 R)
  • M47: 29,315,049 km (0.087 R)
  • M48: 29,751,725 km (0.105 R)
  • M49: 30,897,196 km (0.082 R)
  • M50: 31,519,823 km (0.099 R)
  • M51: 31,788,052 km (0.062 R)
  • M52: 32,416,662 km (0.087 R)
  • M53: 35,064,395 km (0.115 R)
  • M54: 36,554,688 km (0.112 R)
  • M55: 37,118,822 km (0.119 R)
  • M56: 37,875,488 km (0.101 R)
  • M57: 38,255,766 km (0.108 R)
  • M58: 41,440,555 km (0.117 R)
  • M59: 41,734,365 km (0.112 R)
  • M60: 42,028,774 km (0.098 R)
  • M61: 42,916,188 km (0.043 R)
  • M62: 44,408,876 km (0.062 R)
  • M63: 46,121,024 km (0.076 R)
  • M64: 46,222,451 km (0.04 R)
  • M65: 46,425,306 km (0.115 R)
  • M66: 48,162,735 km (0.08 R)
  • M67: 48,781,023 km (0.064 R)
  • M68: 48,987,618 km (0.12 R)
  • M69: 49,401,854 km (0.099 R)
  • M70: 49,609,496 km (0.117 R)
  • M71: 50,547,026 km (0.102 R)
  • M72: 50,756,164 km (0.1 R)
  • M73: 51,280,205 km (0.114 R)
  • M74: 57,053,486 km (0.056 R)
  • M75: 62,916,077 km (0.106 R)
  • M76: 63,141,072 km (0.084 R)
  • M77: 68,967,012 km (0.111 R)
  • M78: 69,314,977 km (0.095 R)
  • M79: 70,595,983 km (0.088 R)
  • M80: 72,709,053 km (0.06 R)
  • M81: 73,654,811 km (0.092 R)
  • M82: 73,891,923 km (0.091 R)
  • M83: 74,129,335 km (0.082 R)
  • M84: 75,200,456 km (0.092 R)
  • M85: 76,756,573 km (0.03 R)
  • M86: 77,117,254 km (0.074 R)
  • M87: 77,237,680 km (0.054 R)
  • M88: 78,928,884 km (0.093 R)
  • M89: 80,144,366 km (0.088 R)
  • M90: 80,388,211 km (0.1 R)
  • M91: 80,999,019 km (0.094 R)
  • M92: 81,366,132 km (0.085 R)
  • M93: 81,611,174 km (0.119 R)
  • M94: 81,856,514 km (0.081 R)

Kuiper Belt

Range: 30 - 56 AU

Composition

Type: Dwarf Planets/TNOs (Ices)

Reservoir of dwarf planets and volatile ices.

Outer System

Oort Cloud

Range: 199 - 18,815 AU

Composition

Type: Cometary Reservoir

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

Gravitational Limit