The U.S. Military Needs to Be Ready to Wage 3 Very Different Types of Wars

U.S. Army Lt. Col. Jonathan Kluck, Commander of the 1st Battalion, 68th Armor Regiment (1–68 Armor), 3rd Armored Brigade Combat Team (3rd ABCT), 4th Infantry Division (4th ID), prepares to dismount his M1A2 Abrams tank after a Combined Arms Live Fire at the 7th Army Training Command’s Grafenwoehr Training Area, Germany, July 31, 2017. (U.S. Army photo by Visual Information Specialist Gertrud Zach)
U.S. Army Lt. Col. Jonathan Kluck, Commander of the 1st Battalion, 68th Armor Regiment (1–68 Armor), 3rd Armored Brigade Combat Team (3rd ABCT), 4th Infantry Division (4th ID), prepares to dismount his M1A2 Abrams tank after a Combined Arms Live Fire at the 7th Army Training Command’s Grafenwoehr Training Area, Germany, July 31, 2017. (U.S. Army photo by Visual Information Specialist Gertrud Zach)

In an article published by The National interest in Oct. 2017, Dave Majumdar cites that, “As rival powers rise to challenge the United States, the Pentagon is faced with the problem of how to face down a spectrum of challenges that range from nuclear deterrence to high-end conventional wars to the low-end counterinsurgency fights.”  How will the Pentagon address all three at the same time? Secretary of Defense, John Mattis, defines it as the Pentagon;s “Problem Statement.” Speaking to an audience at the Association of the U.S. Army Exposition on Oct. 9th, Mattis indicated that “the Defense Department is taking a three-pronged approach to the problem.”

To read more about this approach, visit: http://nationalinterest.org/blog/the-buzz/the-us-military-needs-be-ready-wage-3-very-different-types-22666

The Applied Technology Institute (ATI Courses) offers many short courses on the topics of Radar, Missiles, and Defense, including the following upcoming open enrollments:

See a list of all Radar, Missiles, and Defense courses that ATI offers as open enrollment or on-site.

Examples Of Before and After Imagery That Can Assist In Response Recovery and Rebuilding Operation Planning and Assessment.

As Hurricane Irma churned through the Caribbean and up Florida’s coast,   satellites have been capturing high-resolution images of the storm’s damage. Imaging in the Caribbean became possible over the weekend as the clouds moved out of the area.

Before-and-after imagery taken between Friday, Sept. 8 and Sept. 11 of several places in the Caribbean: Tortola, Turks and Caicos, St Maarten, Necker Island, Barbuda and Saint Martin. The “after” images were taken by Digital Globe’s WorldView-3, WorldView-2 and GeoEye-1 satellites.

Digital Globe has also publicly released pre- and post-event satellite imagery of the areas affected by Hurricane Irma through our Open Data Program, which provides imagery to support recovery efforts in the wake of large-scale natural disasters. Humanitarian Open Street Map Team (HOT) set up mapping tasks for Irma using Digital Globe imagery in preparation for the storm. Additional tasks will be established once more post-event imagery is available, as will a Tomnod crowd sourcing campaign.

 

Port Barbuda PortBarbudaPost StMaartenPreStMaartenPostPhotos credit to the National Oceanic and Atmospheric Administration/Department of Commerce.

Cyberwarfare: US Launched DDoS Attacks Against North Korean Spy Agency

Applied Technology Institute offers a variety of courses on Cyber warfare and Cyber Security.

  1. Cyber Leader Course (CLC)
  2. Cyber Security – Certified Ethical Hacker (CEH)- D124
  3. Cyber Warfare – Global Trends- D131

We think the news below would be of interested to our readers.

The United States has reportedly been engaged in offensive cyber attacks against North Korea, but with no destructive results. According to a report by the Washington Post, President Donald Trump signed a directive earlier this year of putting pressure on North Korea that involved several diplomatic and cyber-military actions, including using cyber activities against the country.

The United States Cyber Command, which was elevated to a Unified Combatant Command by the President earlier this year, targeted North Korea’s military spy agency, the Reconnaissance General Bureau. The attack was a distributed denial of service (DDoS) campaign with an aim to flood North Korean spy agency’s servers with traffic, crippling its access to the internet.

“The elevation of United States Cyber Command demonstrates our increased resolve against cyberspace threats and will help reassure our allies and partners and deter our adversaries,” the White House had said when the President had elevated its status to a combatant unit. “Through United States Cyber Command, we will tackle our cyberspace challenges in coordination with like-minded allies and partners as we strive to respond rapidly to evolving cyberspace security threats and opportunities globally.”

It is unclear when exactly the DDoS attack was launched and how long it lasted, but the Post said that the operation “was due to end” on September 30. The overall campaign – that included a diplomatic campaign to push other countries to sever all ties with Pyongyang – was started in March, this year.

The officials in the US believe that the campaign wasn’t destructive and was merely designed to put pressure on the country. “Nonetheless, some North Korean hackers griped that lack of access to the Internet was interfering with their work,” WaPo reported citing an official. While North Korea isn’t going to find any vocal allies, the latest DDoS attack does make a point that the United States is capable of crippling an adversary’s cyberwar capabilities, even if temporarily.

Russia started providing a second internet route for North Korea, that showed up on Dyn Research according to Security Week. “In effect, it went live with a stable link between Russia and North Korea shortly after the US Cyber Command action finished,” the report adds. Analysts believe that with the DDoS attacks, the US could have had two goals: send a warning to the country and push it to reveal its other channels of internet access or use those that are potentially being monitored.

Some, however, worry that the operation – while not destructive when looked through the US officials’ eyes – might be taken as an act of war by the North Korean administration that could retaliate against the United States using its critical infrastructure that some believe has already been compromised.

Photography Contest for the Midshipmen of the United States Naval Academy

ATI is a supporter and follower of the United States Naval Academy USNA. Several of our instructors are Naval Academy graduates.

The USNA held a photography contest for the midshipmen to highlight their summer training activities around the globe. These are some of the best images. It shows a diversity of places the USNA midshipmen go over their working summer.

http://www.capitalgazette.com/multimedia/photos/cgnews-ac-cn-usna-summer-photo-contest-usna-20170924-pg-photogallery.html

Remote Sensing Before and After Hurricane Harvey

800px-Harvey_2017-08-25_2231ZThe value of remote sensing is shown again with images of before and after Hurricane Harvey. Wow – Take a look!

The Ny times featured Digital Globe images of the areas of Texas that were severely hit by Hurricane Harvey. There are also street level photographs to show the local spots before and after Harvey.

https://www.nytimes.com/interactive/2017/08/29/us/houston-before-and-after-hurricane-harvey.html?mcubz=3

If you are interested in learning more about remote sensing from satellites the Applied Technology Institute (ATIcourses) has in-depth technical training programs.

https://www.aticourses.com/Optical_Communications_Systems.htm

https://www.aticourses.com/synthetic_aperture_radar.html

https://www.aticourses.com/hyperspectral_imaging.htm

The Washington Post has great images of the the rainfall rate relative to historic averages. The claim is that some Texas areas had a rainfall rate that is a 0.1% chance flood event in a year or 1 in 1000 in a year.

“A new analysis from the University of Wisconsin’s Space Science and
Engineering Center has determined that Harvey is a 1-in-1,000-year flood
event that has overwhelmed an enormous section of Southeast Texas
equivalent in size to New Jersey.”

Harvey released 40 inches to 45 inches of rain in a few days over areas of Texas or about 24.5 trillion gallons of water. Huge amount! – that is 3.5 ft in some areas.

https://www.washingtonpost.com/news/capital-weather-gang/wp/2017/08/31/harvey-is-a-1000-year-flood-event-unprecedented-in-scale/

The prediction of the frequency of strong flooding is tricky. The definitions and methods matter and can be slanted to make the author’s point. See the many comments to the above article.

By some measures this is the third 500 year flood in 3 years for Houston.

https://www.washingtonpost.com/news/wonk/wp/2017/08/29/houston-is-experiencing-its-third-500-year-flood-in-3-years-how-is-that-possible/

Please update this post with useful articles about the analysis of the Harvey rainfall and flooding in comparison to other major US flood events.

Updates on GOVERNMENT SHUTDOWN: U.S. BUDGET CRISIS LOOMS (AGAIN IN FY 2018)

Government-ShutdownApplied Technology Institute (ATICourses) provides a variety of technical training courses on Space, Satellite, Radar, Defense, Engineering, Systems Engineering, and Sonar.  Now is the time to plan your training!

This updates an 8/18/2017 post. Unfortunately, the shutdown risk has grown!

This is a good article about the economic cost of a federal shutdown. It provides many detailed examples of the costs of the shutdown caused by the failure of the federal government to act in a timely way due to the shutdown.
https://chiefhro.com/
Jeff Neal was the chief human capital officer at the Homeland Security Department and the chief human resources officer at the Defense Logistics Agency.

Planning training and travel for FY 2018 could be tricky if there is a government shutdown of unknown duration. Many of the people that ATI has talked to have “no remaining FY 2017 training funds and have no idea what training budget will be in the FY 2018”.

The last government shutdown occurred in 2013. The 16-day-long shutdown of October 2013 was the third-longest government shutdown in U.S. history, after the 18-day shutdown in 1978 and the 21-day 1995–96 shutdown. ATI was conducting training in 1995-1996. The 1995 shut-down was chaos.

The last time sequestration kicked in 2013, it forced many federal agencies to furlough employees, costing them up to 20 percent of their salary during the furlough period.  Fortunately, all the government employees were eventually paid their full salary. Paying employees to not work and then rush to catch-up is a wasteful government practice. Many had to struggle until the late salary pay was received.

Standard & Poor’s estimated that the 2013 shutdown took $24 billion out of the U.S. economy, and reduced projected fourth-quarter GDP growth from 3 percent to 2.4 percent.

Even after the shutdown was over there was confusion for several months as employees talked about the shutdown and tried to get all the affected programs back on track. Small businesses and tourist locations lost money that was never recovered. Training and travel funds were devastated for most of the year in 1995 and 2013.

 https://en.wikipedia.org/wiki/United_States_federal_government_shutdown_of_2013

Congress must pass a new government funding bill by Sept. 30 to prevent a shutdown on Oct. 1, which is when fiscal 2018 begins. In previous years, because of the limited amount of time on Capitol Hill in September, lawmakers have been forced to pass a continuing resolution (CR) to keep the government running for a few more months.

This year could be different. “Build that wall,” Mr. Trump said. “Now the obstructionist Democrats would like us not to do it. But believe me, if we have to close down our government, we’re building that wall.”

We’re months away from agreeing on the annual budget, and if Congress and President Trump fail to appropriate funds, government departments won’t be able to spend money. This means contractors won’t get paid.

“If the budget debate gets ugly, which is a clear possibility, we could see the stock shares weaken in September, and then potentially rebound fairly quickly with the conclusion of (or lack of) any shutdown, as was the case in 2013,” Wells Fargo analyst Ed Caso wrote in a Thursday note.

See this link for continuing news updates on the potential 2017 shutdown.

https://federalnewsradio.com/federal-report/2017/08/one-less-thing-to-worry-about-furloughs/

What Could Happen?

During the federal shutdown of 2013, contractor stocks fell as much as 6 percent, while annual revenue and earnings per share were estimated to average a 1- to 1.5-percent hit, according to Wells Fargo. IFCI also lowered guidance.

But this year’s shocks could be amplified.

“We should note that in 2013 the defense sector was at through EV/EBITDA (enterprise value to earnings before interest, taxes, depreciation, and amortization) multiples, while now they are in the upper quartile suggesting the potential for more volatility,” Caso wrote.

But How Worried Should We Be?

Given the current political climate, Caso considers a one-day shutdown possible and a multi-day shutdown modestly likely. Still, the caprice of the Trump administration merits preparation.

“The political calculus, in our view, is even more unstable than in 2013, so uncertainty going into GFY end (September) should only be higher even with the memory that no one gained politically from the 2013 shutdown,” he wrote.

Additionally, the drastic budget changes proposed could sustain debate more contentious than that driving the previous 16-day shutdown. Government agencies and employees do not know how to plan training and travel. Confusion will result for several months.

Army Chief of Staff Orders a Review of EW Shortfalls

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Breaking Defense reports that “Army Chief of Staff Mark Milley, has ordered a review of service’s longstanding shortfalls in electronic warfare, officers told me in an exclusive interview. The ultimate goal: give commanders from platoon to corps the ability to shut down enemy radio and radar as readily as they now call in airstrikes and artillery. It’s a critical part of the Army’s plan to hit future enemies from all possible angles at once, a concept called Multi-Domain Battle.”

Col. Mark Dotson noted that an already apparent issue is the problem that the Army’s current plan to rebuild EW “focuses on combat brigades and neglects higher-level formations, like divisions and corps.”

Col. Chris Walls, a cyber/EW expert on the Army staff, notes that the Army wishes to do the same with the invisible artillery of electronic and cyber warfare that it did, since World War II, “when [they had] mortars, artillery, rockets, attack aviation if I had it, all firing at the target at the same time… to force them to face multiple dilemmas simultaneously.”

ATI offers a variety of EW and EW-related courses, some of which are offered at the end of September 2017. These include:

ELINT Interception and Analysis
September 11–14 2017 in Dayton, OH

Rockets and Launch Vehicles: Selection and Design
September 18–21 2017 in Columbia, MD

C4ISR Requirements, Principles, and Systems
September 19–21 2017 in Columbia, MD

Electronic Warfare Against the New Threat Environment
November 13–16 in Columbia, MD

Radar Systems Fundamentals
November 14–16 in Columbia, MD

Government Shutdown: U.S. Budget Crisis Looms (Again)

Applied Technology Institute (ATICourses) provides a variety of technical training courses on Space, Satellite, Radar, Defense, Engineering, Systems Engineering, and Sonar.  Now is the time to get your training!

Last government shutdown has occurred in 2013.

 https://en.wikipedia.org/wiki/United_States_federal_government_shutdown_of_2013

We’re months away from the annual budget deadline, and if Congress and President Donald Trump fail to appropriate funds, government departments won’t be able to spend money. This means contractors won’t get paid.

“If the budget debate gets ugly, which is a clear possibility, we could see the shares weaken in September, and then potentially rebound fairly quickly with the conclusion of (or lack of) any shutdown, as was the case in 2013,” Wells Fargo analyst Ed Caso wrote in a Thursday note.

However, those with fixed-price contracts, higher exposure to the Defense or Homeland Security Departments, or more off-site work are considered to be at a lesser risk.

What Could Exactly Happen?

During the federal shutdown of 2013, contractor stocks fell as much as 6 percent, while annual revenue and earnings per share were estimated to average a 1- to 1.5-percent hit, according to Wells Fargo. IFCI also lowered guidance.

But this year’s shocks could be amplified.

“We should note that in 2013 the sector was at through EV/EBITDA (enterprise value to earnings before interest, taxes, depreciation, and amortization) multiples, while now they are in the upper quartile suggesting the potential for more volatility,” Caso wrote.

But How Worried Should We Be?

Given the current political climate, Caso considers a one-day shutdown possible and a multi-day shutdown modestly likely. Still, the caprice of the Trump administration merits preparation.

“The political calculus, in our view, is even more unstable than in 2013, so uncertainty going into GFYend (September) should only be higher even with the memory that no one gained politically from the 2013 shutdown,” he wrote.

Additionally, the drastic budget changes proposed could sustain debate more contentious than that driving the previous 16-day shutdown.

 

Girl Power Playlist: Guess The Top Songs

IMG_5166 (2)

Here’s A Power Boost

For all the women in our lives who need a power boost of encouragement, this Girl Power Album Playlist is for you!

It’s for smart and courageous young ladies like my nieces (Ivy & Eden) and my daughters (Alice & Quinn). It also goes for the ladies like Jim’s daughter Julie.  Julie and my nieces are breaking down barriers in traditionally masculine fields. Julie is now a practicing law for the  VA in Washington, DC.   Ivy and Eden are enrolled in honors pharmaceutical and law programs where girls are outnumbered four to one (as they often are in science, technology, engineering, and math).   Alice & Quinn are too young to demonstrate their intellectual prowess, but nevertheless, every day they demonstrate that they are gritty as well as pretty.

This is a list of the top 10 Girl Power Albums in alphabetical order.

Pick your favorite top 3 and guess what 3 National Public Radio selected as the greatest albums.  The answers are below, but pick you favorite first.  You can email it to ati@aticourses.com.  We will post your votes.

Amy Winehouse
Back To Black (Island, 2006)

Aretha Franklin
I Never Loved a Man The Way I Love You (Atlantic, 1967)

Beyoncé
Lemonade (Parkwood/Columbia, 2016)

Carole King

  1. Tapestry(Ode, 1971)

Janis Joplin
Pearl (Columbia, 1971)

Joni Mitchell
Blue (Reprise, 1971)

 Lauryn Hill
The Miseducation of Lauryn Hill (Ruffhouse/Columbia, 1998)

 Missy Elliott
Supa Dupa Fly (The Goldmind/Elektra, 1997)

Nina Simone
I Put A Spell on You (Philips, 1965)

Patti Smith
Horses (Arista, 1975)

Lastly, this female empowerment playlist is a shout-out to women like my mother and sister-in-law who have assumed care giving roles.  Unless you’ve walked in those shoes or witnessed the work that goes into such care taking, it’s hard to truly appreciate the investment of time, resources, and emotional energy.

Why not make a custom album list to encourage the special women in your life — or yourself — to keep being brave, strong, and fighting

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Processed with VSCO with p5 preset

the good fight?

 


10. Carole King
Tapestry (Ode, 1971)

With Tapestry, Carole King cemented her place as one of the key architects of 20th-century popular music. Here, she fully claims the spotlight, not only as a top-notch composer, but as a deeply soulful lyricist and singer.


9. Amy Winehouse
Back To Black (Island, 2006)

The late ’00s saw an explosive, cross-genre revival of retro-sounding soul music that continues to shape the pop landscape to this day. Arguably, that trend’s catalyst was Amy Winehouse‘s earth-shaking final album.


8. Janis Joplin
Pearl (Columbia, 1971)

One of rock’s most misunderstood artists, Janis Joplinwas often portrayed as victim, a dysfunctional mess who only fronted a band, who didn’t have the power to call the shots. Until Pearl. In 1971, with Monterey Pop, Woodstock, and Festival Express behind her, the vision of blues, rock and soul coming together with a band that could follow her was realized. It was her high point, and tragically, she didn’t live to see it. Janis had put the band together — saying “it’s my band, it’s finally my band” — and approved all the songs. (It was unusual at the time for a female artist to actually have that control, the very reason we need this list.)


7. Patti Smith
Horses (Arista, 1975)

The very nature of Patti Smith‘s debut album Horsesrails against what many other “best of” albums are celebrated for — broad appeal, sonically pleasing aesthetics and hits. Horses is confrontational, defiant and completely unafraid of the ugly.


6. Beyoncé
Lemonade (Parkwood/Columbia, 2016)

One of the most recent projects to be part of our new canon, Lemonade is a masterful excursion through terrains at once visually fantastical and emotionally all too real, exploring shattered trust in a broken relationship; the singular pain borne by the mothers of men like Trayvon Martin, Eric Garner and Michael Brown; the battering down of black women throughout history; the scars of all of these kinds of trauma; white-hot rage and hopeful, though not blind, reconciliation.


5. Missy Elliott
Supa Dupa Fly (The Goldmind/Elektra, 1997)

This album dismantled the hip-hop boy’s club. For the first time in history a woman rapped, sang, wrote and produced every song on a major rap release. Within the first sounds that we hear, Missy Elliott invites you to become engulfed with the undeniable Virginia-based funk, a region that’s equally Southern and Eastern, through aquatic synth sounds paired with earthy drum patterns.


4. Aretha Franklin
I Never Loved a Man The Way I Love You (Atlantic, 1967)

In the universe of popular music, this album exploded like a brand new sun. It took Aretha Franklin eleven songs to shift the canon of AM radio away from the realm of girlish glee to the cataclysms of womanly love. I Never Loved a Man connected with black and white audiences and became the biggest commercial success of her building career.


3. Nina Simone
I Put A Spell on You (Philips, 1965)

Nina Simone knew her own power. Not only did she cover the song “I Put A Spell on You,” but she also used it as the title of her autobiography. The song, originally released in 1956 by Jay Hawkins, cemented his “Screamin” moniker. But in Simone’s hands, it became something more, a kind of simmering sorcery.


2. Lauryn Hill
The Miseducation of Lauryn Hill (Ruffhouse/Columbia, 1998)

The Fugees struck gold in the late 1990s with albums like The Score, a feat that also made their resident wordsmith, Lauryn Hill, a household nameBut when Hill went out on her own two years later and dropped her debut, the neo-soul masterpiece The Miseducation of Lauryn Hill, she schooled everyone all over again in new and necessary ways.


1. Joni Mitchell
Blue (Reprise, 1971)

After nearly fifty years, Blue remains the clearest and most animated musical map to the new world that women traced, sometimes invisibly, within their daily lives in the aftermath of the utopian, dream-crushing 1960s. It is a record full of love songs, of sad songs; but more than that, it is a compendium of reasonable demands that too many men in too many women’s lives heard, in 1971, as pipe dreams or outrageous follies.

List of top in count-down order.

GREAT OLD, BIG, HUGE BLACK HOLES

In 1905 Albert Einstein employed one of the most powerful brains on planet Earth to puzzle out an elusive concept called “The Special Theory of Relativity”.  Ten years later he used those same brain cells to develop his even more powerful “General Theory of Relativity”.

Figure 1 highlights his most dramatic proposal for proving – or disproving! – his General Theory of Relativity.  The test he proposed had to take place during a total eclipse of the sun.  For, according to The General Theory of Relativity, light from a more distant star would be bent by about one two-thousandths of a degree when it swept by the edge of the sun.

Four years later (in 1919) the talented British astronomer Arthur Eddington in pursuit of a total eclipse of the sun, ventured to the Crimean Peninsula to perform the test Einstein had proposed based on the idea that “starlight would swerve measurably as it passed through the heavy gravity of the sun, a dimple in the fabric of the universe.”*

A black hole comes into existence when a star converts all of its hydrogen into helium and collapses into a much smaller ball that is so dense nothing can escape from its gravitational pull, not even light.

Capture3

Figure 1:  In 1915, when he finally worked out his General Theory of Relativity, Albert Einstein proposed three clever techniques for testing its validity.  Four years later, in 1919 the British astronomer, Arthur Eddington, took advantage of one of those tests during a total eclipse of the sun to demonstrate that, when a light beam passes near a massive celestial body, it is bent by the local gravitational field as predicted by Einstein’s theory.  This distinctive bending is similar to the manner a baseball headed toward home plate is bent downward by the gravitational pull of the earth.

The existence of black holes was inadvertently predicted by a mathematical relationship Sir Isaac Newton understood and employed in 1687 in developing many of his most powerful scientific predictions, including the rather weird concept of escape velocity.  As Figure 2 indicates, it is called the Vis Viva equation.

Start by solving the Vis Viva equation for the radius Re, then plug in the speed of light, C, as a value for the escape velocity, Ve.  The resulting radius Re is the so-called “event horizon”, which equals the radius at which light cannot escape from an extremely dense sphere of mass, M.  As the calculation on the right-hand side of Figure 2 indicates, if we could somehow compressed the earth down to a radius of 0.35 inches – while preserving its total mass light waves inside the sphere would be unable to escape and, therefore, could not be seen by an observer.  The radius of the event horizon associated with a spherical body of mass, M, is directly proportional to the total mass involved.

Capture4

Figure 2:  The Vis Viva equation was developed and applied repeatedly by Isaac Newton when he was evaluating various gravity-induced phenomena.  Properly applied, the Vis Viva equation predicts that sufficiently dense celestial bodies generate such strong gravitational fields that nothing – not even a beam of light – can escape their clutches.  Today’s astronomers are discovering numerous examples of this counterintuitive effect.  Black holes are one result.

As Figure 3 indicates, an enormous black hole 50 million light years from Earth has been discovered to have a mass equal to 2 billion times the mass of our sun.   It is located in the M87 Galaxy in the constellation Virgo.

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Figure 3:  In 1994 the Hubble Space Telescope discovered a huge black hole approximately 300,000,000,000,000,000,000,000 miles from planet Earth nestled among the stars of the M87 galaxy in the Virgo constellation.  Astronomers estimate that it is 2,000,000,ooo times heavier than our son.  That black hole’s event horizon has a radius of 3,700,000,000 miles or about 40 astronomical units. One astronomical unit being the distance from the earth to our sun.The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

See all the ATI open-enrollment course schedule

https://www.aticourses.com/schedule.html

See all the ATI courses on 1 page.

What courses would you like to see scheduled as an open-enrollment or on-site course near your facility?

ATI is planning its schedule of technical training courses and would like your recommendations of courses

that will help your project and/or company.

These courses can also be held on-site at your facility.

http://www.aticourses.com/catalog_of_all_ATI_courses.htm