The Torino scale is a method for categorizing the impact hazard associated with near-Earth objects (NEOs) such as asteroids and comets. It is intended as a communication tool for astronomers and the public to assess the seriousness of collision predictions, by combining probability statistics and known kinetic damage potentials into a single threat value. The Palermo Technical Impact Hazard Scale is a similar, but more complex scale. Near-Earth objects with a Torino scale of 1 pop up every couple of months or so and may last a few weeks until they have a longer observation arc.
1. Overview
Torino Scale. The scale in metres is the approximate diameter of an asteroid with a typical collision velocity. https://handwiki.org/wiki/index.php?curid=2086874
The Torino Scale uses an integer scale from 0 to 10. A 0 indicates an object has a negligibly small chance of collision with the Earth, compared with the usual "background noise" of collision events, or is too small to penetrate Earth's atmosphere intact. A 10 indicates that a collision is certain, and the impacting object is large enough to precipitate a global disaster.
An object is assigned a 0 to 10 value based on its collision probability and the kinetic energy (expressed in megatons of TNT) of the possible collision.
The Torino Scale is defined only for potential impacts less than 100 years in the future.
"For an object with multiple potential collisions on a set of dates, a Torino Scale value should be determined for each date. It may be convenient to summarize such an object by the greatest Torino Scale value within the set."[1]
2. History and Naming
The Torino Scale was created by Professor Richard P. Binzel in the Department of Earth, Atmospheric, and Planetary Sciences, at the Massachusetts Institute of Technology (MIT). The first version, called "A Near-Earth Object Hazard Index", was presented at a United Nations conference in 1995 and was published by Binzel in the subsequent conference proceedings (Annals of the New York Academy of Sciences, volume 822, 1997.)
A revised version of the "Hazard Index" was presented at a June 1999 international conference on NEOs held in Torino (Turin), Italy. The conference participants voted to adopt the revised version, where the bestowed name "Torino Scale" recognizes the spirit of international cooperation displayed at that conference toward research efforts to understand the hazards posed by NEOs. ("Torino Scale" is the proper usage, not "Turin Scale.")[1]
Due to exaggerated press coverage of Level 1 asteroids, a rewording of the Torino Scale was published in 2005, adding more details and renaming the categories: in particular, Level 1 was changed from "Events meriting careful monitoring" to "Normal".
The Torino Scale has served as the model for the Rio scale which quantifies the validity and societal impact of SETI data.[2]
3. Current Torino Scale
The Torino Scale also uses a color code scale: white, green, yellow, orange, red. Each color code has an overall meaning:[3]
NO HAZARD (white) |
0 |
The likelihood of a collision is zero, or is so low as to be effectively zero. Also applies to small objects such as meteors and bodies that burn up in the atmosphere as well as infrequent meteorite falls that rarely cause damage. |
NORMAL (green) |
1 |
A routine discovery in which a pass near Earth is predicted that poses no unusual level of danger. Current calculations show a collision is extremely unlikely with no cause for public attention or public concern. New telescopic observations very likely will lead to reassignment to Level 0. |
MERITING ATTENTION BY ASTRONOMERS (yellow) |
2 |
A discovery, which may become routine with expanded searches, of an object making a somewhat close but not highly unusual pass near Earth. While meriting attention by astronomers, there is no cause for public attention or public concern as an actual collision is very unlikely. New telescopic observations very likely will lead to reassignment to Level 0. |
3 |
A close encounter, meriting attention by astronomers. Current calculations give a 1% or greater chance of collision capable of localized destruction. Most likely, new telescopic observations will lead to reassignment to Level 0. Attention by public and by public officials is merited if the encounter is less than a decade away. |
4 |
A close encounter, meriting attention by astronomers. Current calculations give a 1% or greater chance of collision capable of regional devastation. Most likely, new telescopic observations will lead to reassignment to Level 0. Attention by public and by public officials is merited if the encounter is less than a decade away. |
THREATENING (orange) |
5 |
A close encounter posing a serious, but still uncertain threat of regional devastation. Critical attention by astronomers is needed to determine conclusively whether a collision will occur. If the encounter is less than a decade away, governmental contingency planning may be warranted. |
6 |
A close encounter by a large object posing a serious but still uncertain threat of a global catastrophe. Critical attention by astronomers is needed to determine conclusively whether a collision will occur. If the encounter is less than three decades away, governmental contingency planning may be warranted. |
7 |
A very close encounter by a large object, which if occurring this century, poses an unprecedented but still uncertain threat of a global catastrophe. For such a threat in this century, international contingency planning is warranted, especially to determine urgently and conclusively whether a collision will occur. |
CERTAIN COLLISIONS (red) |
8 |
A collision is certain, capable of causing localized destruction for an impact over land or possibly a tsunami if close offshore. Such events occur on average between once per 50 years and once per several thousand years. |
9 |
A collision is certain, capable of causing unprecedented regional devastation for a land impact or the threat of a major tsunami for an ocean impact. Such events occur on average between once per 10,000 years and once per 100,000 years. |
10 |
A collision is certain, capable of causing global climatic catastrophe that may threaten the future of civilization and wildlife as we know it, whether impacting land or ocean. Such events occur on average once per 100,000 years, or less often. |
No incoming object has ever been rated above level 4, though over all of Earth's history impacts have spanned the full range of damage described by the scale.
4. Actual Impacts and Impact Energy Comparisons
The Chicxulub impact, believed by most scientists to have been a significant factor in the extinction of the non-avian dinosaurs, has been estimated at 100 million (108) megatons, or Torino Scale 10. The impacts which created the Barringer Crater and the 1908 Tunguska event are both estimated to be in the 3–10 megaton range,[4] corresponding to Torino Scale 8. The 2013 Chelyabinsk meteor had a total kinetic energy prior to impact of about 0.5 megatons, corresponding to Torino Scale 0. Between 2000 and 2013, 26 asteroid impacts with an energy of 1–600 kilotons were detected.[5]
The biggest hydrogen bomb ever exploded, the Tsar Bomba, was around 50 megatons. The 1883 eruption of Krakatoa was the equivalent of roughly 200 megatons.
The comet C/2013 A1, which passed close to Mars in 2014, was originally estimated to have a potential impact energy of 5 million to 24 billion megatons, and in March 2013 was estimated to have a Mars impact probability of ~1:1250, corresponding to the Martian equivalent of Torino Scale 6.[6] The impact probability was reduced to ~1:120000 in April 2013, corresponding to Torino Scale 1 or 2.[7]
5. Objects with Non-Zero Torino Ratings
5.1. Downgraded to Zero
This is a partial list of near-Earth asteroids that have been listed with a Torino Scale rating of 1+ and been lowered to 0 or been removed from the Sentry Risk Table altogether. Most objects that reach a Torino Scale of 1 have a short observation arc of less than 2 weeks and are quickly removed as the observation arc gets longer and more accurate.
- 2002
- (163132) 2002 CU11 was rated level 1 on 20 March 2002,[8] and completely removed from the Sentry Risk Table on 26 April 2002.[9]
- (89959) 2002 NT7 was rated level 1 on 24 July 2002,[10] and was removed from the risk table on 1 August 2002.[9]
- 2003
- (177049) 2003 EE16 was rated level 1 on 2 April 2003,[11] and removed from the risk table on 28 May 2003.[9]
- (387746) 2003 MH4 was rated level 1 on 7 July 2003 with an observation arc of 10 days.[12] There was roughly an estimated 1 in 19,000 chance of impact on 9 June 2077.[12] It was removed from the risk table on 29 July 2003.[9]
- (143649) 2003 QQ47 was rated level 1 on 30 August 2003[13] and removed from the Sentry Risk Table on 14 September 2003.[9]
- (143651) 2003 QO104 was rated level 1 in early October 2003,[14] and removed on 13 October 2003.[9]
- (164121) 2003 YT1 was rated level 1 on 27 December 2003 with an observation arc of 8.7 days.[14] It was removed from the risk table on 29 December 2003.[9]
- 2004
- (144332) 2004 DV24 was rated level 1 on 1 March 2004 with an observation arc of 7.8 days.[15] It was removed on 5 March 2004.[9]
- (497117) 2004 FU4 was rated level 1 on 27 March 2004 with an observation arc of 6.9 days.[16] It was lowered to 0 on 2 April 2004. It was removed on 13 April 2004.[9]
- (99942) Apophis (a near-Earth asteroid 370 meters in diameter) became the first object rated level 2 on 23 December 2004,[17] and was subsequently upgraded to level 4 — the current record for highest Torino rating.[17] (It is now known Apophis will pass 38000 km from Earth on 13 April 2029.) It retained a rating of level 1 for a 2036 approach due to the prior orbital uncertainties introduced by the close approach of 2029. In August 2006 Apophis was downgraded to 0. In 2021 Apophis was removed from the risk-list.
- 2005
- No asteroids reached Torino scale 1 in 2005.
- 2006
- (144898) 2004 VD17 (using an observation arc of 475 days) was upgraded to level 2 in February 2006 for a possible 2102 encounter, making it the second asteroid rated above level 1.[18] It was downgraded to 0 after further observations. It was removed from the Sentry Risk Table on 14 February 2008.[9]
- (433953) 1997 XR2 was a lost asteroid from December 1997 that had an observation arc of 27 days.[19] From early 2002 until 24 February 2006 it was estimated to have a 1 in 10,000 chance of impacting Earth on June 1, 2101.[19] It was removed from the risk table on 24 February 2006 when it was serendipitously rediscovered.[9]
- (292220) 2006 SU49 (with an observation arc of 7 days) showed a 1 in 42000 chance of impacting Earth on 22 January 2029.[20] It was removed from the Sentry Risk Table on 23 November 2006.[9]
- (417634) 2006 XG1 was rated level 1 on December 22, 2006, when it had an observation arc of 25 days,[21] but was removed from the Sentry Risk Table on February 7, 2007.[9]
- 2007
- (481482) 2007 CA19 was rated level 1[22] for one week ending 19 February 2007. The asteroid was estimated to be roughly 970 meters (3,180 ft) in diameter and had a virtual impactor listing a 1 in 625,000 chance of impact on 14 March 2012.[22] It was removed from the risk table on February 22.[9]
- (435159) 2007 LQ19 was rated level 1 on 3 July 2007 with an observation arc of 19 days.[23] The asteroid was estimated to be 930 meters (3,050 ft) in diameter and there was a 1 in 556,000 chance of impact on 11 July 2082.[23] It was removed from the risk table on 15 July 2007.[9]
- 2008
- (332446) 2008 AF4 was rated level 1[24] until 14 February 2008. It was removed from the risk table on 19 December 2009.[9]
- 2009
- 2009 KK was rated level 1 after its discovery in May 2009 (with a 15-day observation arc),[25] and downgraded to 0 by 11 June 2009. It was removed 17 June 2009.[9]
- 2009 WM1 was rated level 1 after its discovery on 17 November 2009,[26] and downgraded by the end of November. It was not removed from the risk table until 26 June 2013.[9]
- (359369) 2009 YG was rated level 1 on 28 December 2009 (with an observation arc of 10 days).[27] It was downgraded to 0 by the end of December.
- 2010
- (308635) 2005 YU55 was rated level 1 in February 2010,[28] and downgraded to 0 on 9 April 2010. The chance of an actual collision with an asteroid like 2005 YU55 (~400 meters in diameter) is about 1 percent in the next thousand years.[29]
- (494999) 2010 JU39 was rated level 1 on 18 May 2010 with an observation arc of 7 days.[30] There was roughly an estimated 1 in 77,000 chance of impact on 26 June 2058.[30] It was removed on 23 May 2010.[9]
- 2010 XC25 was rated level 1 in December 2010, and downgraded to 0 on 2 January 2011.[31]
- 2011
- 2011 BM45 was rated level 1 on 13 February 2011 with an observation arc of 13.8 days.[32] There was a 1 in 24,000 chance of impact on 18 January 2086.[32] It was removed from the risk table on 10 March 2011.[9]
- 2011 SM68 was rated level 1 on 28 September 2011 with an observation arc of 2.6 days and listed virtual impactors in 2016 and 2019.[33] But it was quickly downgraded to 0 a few days later and was removed from the risk table on 7 October 2011.[9]
- (415029) 2011 UL21 is an asteroid with a diameter of 2.6 km, which was rated level 1 on October 27, 2011 (with an observation arc of 9.6 days.)[34] It was downgraded to 0 a few days later.
- (436724) 2011 UW158 was rated level 1 on 4 November 2011 with an observation arc of 9 days.[35] There was a 1 in 56,000 chance of impact on 8 July 2079.[35] It was removed 17 November 2011.[9]
- 2012
- 2012 CA21 was rated level 1 on 21 February 2012 (with an observation arc of 8.9 days).[36] It was removed from the risk table on 3 March 2012.[9]
- 2012 MU2 was rated at Torino scale 1 on 23 June 2012 with an observation arc of 4 days.[37] With an observation arc of only 6 days it showed a 1 in 7140 chance of impact on 1 June 2015. It was removed from the Sentry Risk Table on June 25.[9]
- (367789) 2011 AG5 was rated at Torino scale 1 from February 2011 to December 2012, for an impact on 5 February 2040.[38] It was downgraded thanks to observations collected in October 2012 with telescopes on Mauna Kea, Hawaii.
- 2013
- 2013 TV135 (a near-Earth asteroid with a 450 m diameter) was rated level 1 on 16 October 2013 (with an observation arc of 7.3 days).[39] It was downgraded to 0 on 3 November 2013.[40] It was completely removed from the Sentry Risk Table on 8 November 2013 using JPL solution 32 with an observation arc of 27 days.[9]
- 2014
- 2014 DA with an estimated diameter of 100 meters was rated level 1 on 23 February 2014 with an observation arc of 5 days. It was estimated to have a 1 in 5,560 chance of impact on 2 February 2027.[41] It was lowered to Torino Scale 0 on the next day (24 February 2014).[42]
- 2007 VK184 was listed on the Near Earth Object Risk List with a Torino Scale of Level 1[43] from after its discovery in November 2007 until recovered in March 2014. With an observation arc of 60 days, it had about a 1 in 1800 chance of impacting Earth on 3 June 2048; the probability went to effectively zero when the 2014 recovery observations were taken into account. The asteroid is estimated to have a diameter of 130 meters (430 ft), and travels through space with a speed of 15.6 km/s relative to Earth.
- 2015
- 2015 NK13 was listed on the JPL Near Earth Object Risk List with a Torino Scale of Level 1 on 22 July 2015 and again on 11 August 2015,[44] while the NEODyS Risk List had it at a slightly lower impact probability, sufficient to classify it as Torino Scale Level 0. In July and August it was downgraded to Level 0 the following day. With a 13-day observation arc, it had an estimated 1 in 36,000 chance of impacting Earth on 5 October 2096.[44] It was discovered on 12 July 2015 by Pan-STARRS.[45] The asteroid is estimated to have a diameter of 310 meters (1,020 ft), and would impact Earth at a relative speed of 14.35 km/s (32,000 mph).[44]
- 2015 PU228 was listed on NEODyS with a Torino Scale of Level 1 on 23 August 2015.[46] Sentry also listed it with a Torino Scale of Level 1 on 24 August 2015.[47] With a 10-day observation arc, it had an estimated 1 in 84,000 chance of impacting Earth on 15 January 2081.[46] It was downgraded to level 0 on 8 September 2015. It was discovered on 13 August 2015 by the Space Surveillance Telescope.[48] The asteroid is estimated to have a diameter of 340 meters (1,120 ft).
- 2016
- 2016 BE was rated at level 1 for a day on 25 January 2016 by the NEODyS system, and downgraded to level 0 the following day. On the Sentry system it never crossed the threshold between the two levels, due to a lower computed impact probability.
- 2016 EU85 was rated at level 1 by NEODyS on 25 March 2016, but subsequently lowered to zero thanks to prediscovery observations by the Pan-STARRS survey. The asteroid is estimated to have a diameter of about 440 meters (1,440 ft).
- 2016 WJ1 was listed on the JPL Near Earth Object Risk List with a Torino Scale of Level 1 on 25 November 2016,[49] while the NEODyS Risk List has it at a lower impact probability, sufficient to classify it as Torino Scale Level 0. With a 10-day observation arc, it had an estimated 1 in 8000 chance of impacting Earth on 12 June 2065.[49] It was discovered on 19 November 2016 by Mt. Lemmon Survey.[50] The asteroid is estimated to have a diameter of 180 meters (590 ft), and would have impacted Earth at a relative speed of 18.61 km/s (42,000 mph).[49] It was removed from the Sentry Risk Table on 2 December 2016, when prediscovery images by Pan-STARRS from October 2016 and precovery images taken from Mauna Kea in July 2003 where located and included in the impact calculations.
- 2016 XP23 was listed on the JPL Near Earth Object Risk List with a Torino Scale of Level 1 on 25 December 2016,[51] while the NEODyS Risk List has it at a lower impact probability, sufficient to classify it as Torino Scale Level 0. With a 15-day observation arc, it was listed with an estimated 1 in 105,000 chance of impacting Earth on 1 November 2110.[51] The asteroid is estimated to have a diameter of 360 meters (1,180 ft), and would have impacted Earth at a relative speed of 27 km/s (60,000 mph).[51] It was removed from the Sentry Risk Table on 7 January 2017 with a 29-day observation arc.
- 2017
- 2017 AM4 was listed on the JPL Near Earth Object Risk List and NEODyS Risk List with a Torino Scale of Level 1 on 19 January 2017.[52] With a 14-day observation arc, it had an estimated 1 in 59,000 chance of impacting Earth on 1 August 2024.[52] The asteroid is estimated to have a diameter of 500 meters (1,600 ft), and would impact Earth at a relative speed of 33 km/s (74,000 mph).[52] With a 16-day observation arc, the odds of impact were reduced to 1 in a million. It was removed from the Sentry Risk Table on 23 January 2017 with a 19-day observation arc.
- 2017 BL30 was listed on the JPL Near Earth Object Risk List and NEODyS Risk List with a Torino Scale of Level 1 on 3 February 2017.[53] With a 5-day observation arc, it had an estimated 1 in 1610 chance of impacting Earth on 3 August 2029.[53] With a 6-day observation arc, the odds were 1 in 1270.[53] With a 7-day observation arc, the odds were 1 in 909.[53] With a 10-day observation arc, the odds were 1 in 826.[53] The asteroid is estimated to have a diameter of 70 meters (230 ft), and would impact Earth at a relative speed of 13 km/s (29,000 mph).[53] The value decreased to 0 with further observations on February 11, with a cumulative impact chance of 1 in 4258.
- 2017 CH1 was listed on the NEODyS Risk List with a Torino Scale of Level 1 on 8 February 2017.[54] It is estimated be 900 meters in diameter with a 1 in 500000 chance of impact on 4 June 2095.[54] Such an impact could create a crater 10 km in diameter.[55] Follow-up observations on February 10 eliminated the chances of impact on every date except for 4 June 2044, with a 4.59E-10 chance of impact on that date, or less than a 1 in 2 billion chance of impact. It was removed from the Sentry Risk Table on 15 February 2017.
- 2018
- 2017 YZ1 was listed on the JPL Near Earth Object Risk List and NEODyS Risk List with a Torino Scale of Level 1 on 5 January 2018. With a 15-day observation arc, it had an estimated 1 in 21000 chance of impacting Earth on 30 June 2047. The asteroid is estimated to have a diameter of 260 meters (850 ft), and would impact Earth at a relative speed of 18 km/s (40,000 mph). By 9 January 2018 the geocentric 30 June 2047 uncertainty region had shrunk to ±50 million km. After calculations based on a 20-day observation arc were made, chances of impact on 30 June 2047 dropped to 1 in 670000, and 2017 YZ1 was downgraded to Level 0.
- 2017 XO2 was listed on the JPL Near Earth Object Risk List with a Torino Scale of Level 1 as of 20 January 2018. With a 40-day observation arc, it had an estimated 1 in 3000 chance of impacting Earth on 28 April 2057.[56] The asteroid is estimated to have a diameter of about 110 meters (360 ft). The nominal 2057 Earth approach distance was estimated at 0.001 au (100,000 km; 90,000 mi) with a 3-sigma uncertainty of ±52 million km. On 27 January 2018 Pan-STARRS precovery images from November and December 2011 were announced, and 2017 XO2 was removed from the Sentry Risk Table.
- 2018 GG2 (diameter ~480 meters) with a 7-day observation arc showed a 1 in 270,000 chance of impact on 5 April 2111 using the 17 April 2018 orbit solution.[57] Later on the same day it was removed from the Sentry Risk Table as a result of precovery images dating back to 24 September 2017 extending the observation arc to 205 days.
- 2018 LB1 was removed from the Sentry monitoring list on 14 June 2018[58] after having been on the Risk List with a Torino Scale of Level 1.
- 2019
- No asteroids reached Torino scale 1 in 2019.
- 2020
- 2020 BW14 (diameter ~700 meters) with a 13-day observation arc showed a 1 in 180,000 chance of impact on 14 October 2046.[59] But the nominal solution had the asteroid 0.7 AU (100 million km) from Earth on 14 October 2046. It was removed from the Sentry monitoring list on 10 February 2020 with 19 precovery images from January to April 2016.[60]
- 2020 DR2 (diameter ~590 meters) with a 15-day observation showed a 1 in 290,000 chance of impact on 10 September 2074 and showed a 1 in 77,000 chance of impact on 9 September 2081.[61] Cumulatively, this gave the asteroid a 1 in 59,000 chance of impact in the next century. The asteroid was downgraded to 0 after its arc was extended to 16 days with a 1 in 500,000 cumulative chance of impact. It was removed from the sentry risk table entirely on 11 March 2020.
- 2020 NK1 (diameter ~600 meters) initially showed, with a 7.6 day observation arc, a 1 in 83,000 chance of impact on 3 August 2093.[62] With a 11.2 day observation arc, the odds decreased to 1 in 7.1 million. However, the odds of an impact on 4 August 2104 increased to 1 in 45,000.[62] With a 13.2 day observation arc, the 2104 impact was ruled out, but a 4 August 2101 impact became more probable, with the odds increasing to 1 in 36,000.[62] The nominal distance from Earth on 4 August 2101 is 0.87 AU (130 million km). It was removed from the sentry risk table entirely on July 31 with a 15.6 day observation arc.
- 2020 XR (diameter ~390 meters) with a 5 day observation arc showed a 1 in 11,000 chance of impact on 1 December 2028[63] and a nominal distance from Earth on 1 December 2028 of 0.16 AU (24 million km; 62 LD) with an uncertainty region of ±304 million km. The 8 day observation arc showed a 1 in 26,000 chance of impact on 1 December 2028 and a nominal distance from Earth on 1 December 2028 of 1 AU (150 million km; 390 LD). On 13 December 2020 precovery observations from 2013, 2016, and mid-2020 extended the observation arc from 8 days to 7.8 years allowing the asteroid to be removed from the Sentry Risk Table.
- 2021
- 2021 TA8 (diameter ~200 meters) with a 7.6 day observation arc showed a 1 in 6,700 chance of impact on 3 May 2034.[64] With a 7 day arc, the nominal distance from Earth on 3 May 2034 was 0.03 AU (4.5 million km) with an uncertainty region of ±20 million km.[65] It was removed from the ESA and Sentry Risk Table on 12 October 2021 when precovery images from 2010, 2015 and 2018 were located in the DECam and Pan-STARRS archives.
- 2021 TP21 (diameter ~300 meters) with a 18.9 day observation arc showed a 1 in 56,000 chance of impact on 27 March 2081.[66] The nominal distance from Earth on 27 March 2081 was estimated at 1.4 AU (210 million km) with an uncertainty region of ±870 million km.[67] It was removed from the Sentry risk list on 4 November 2021 with a 57 day observation arc and a nominal approach of 2.5 AU with an uncertainty region of ±18 million km.
- 2022
- 2022 AE1 (diameter ~70 meters) with a 3-8 day observation arc showed about a 1 in 2,000 chance of impact (18 months later) on 4 July 2023.[68] The nominal distance from Earth on 4 July 2023 was estimated as small as 0.024 AU (3.6 million km) with an uncertainty region of ±38 million km. It was lowered to Torino Scale 0 on 20 January 2022 with a 16 day observation arc and a nominal approach of 7.9 million km.
- 2022 BX1 (diameter ~160 meters) with a 22 day observation arc showed a 1 in 7,700 chance of impact on 11 July 2061.[69] It was lowered to Torino Scale 0 with a 24 day observation arc. The nominal distance from Earth on 11 July 2061 is 0.14 AU (21 million km) with an uncertainty region of ±600 thousand km.[70]
- 2022 QX4 (diameter ~40 meters) with a 8 day observation arc showed a 1-in-109 chance of impact on 4 September 2068.[71] The nominal distance from Earth on 4 September 2068 is now known to be 0.047 AU (7.0 million km) with an uncertainty region of ±32 thousand km.[72]
The content is sourced from: https://handwiki.org/wiki/Astronomy:Torino_scale