, in meters (based on the EGM96 gravity model and the WGS84 reference ellipsoid).]]

The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest (relative to the rotating Earth), and extended through the continents (such as with very narrow canals). According to C.F. Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations. Despite being an important concept for almost two hundred years in the history of geodesy and geophysics, it has only been defined to high precision in recent decades, for instance by works of Petr Vaníček and others. It is often described as the true physical figure of the Earth, in contrast to the idealized geometrical figure of a reference ellipsoid.

Description

[[Image:Geoida.svg|thumb|right|350px|1. Ocean 2. Reference ellipsoid 3. Local plumb line 4. Continent 5. Geoid]] The geoid surface is irregular, unlike the reference ellipsoid which is a mathematical idealized representation of the physical Earth, but considerably smoother than Earth's physical surface. Although the physical Earth has excursions of +8,000 m (Mount Everest) and −11,000 m (Mariana Trench), the geoid's total variation is less than 200 m (−106 to +85 m) compared to a perfect mathematical ellipsoid.

Sea level, if undisturbed by tides, currents and weather, would assume a surface equal to the geoid. If the continental land masses were criss-crossed by a series of tunnels or narrow canals, the sea level in these canals would also coincide with the geoid. In reality the geoid does not have a physical meaning under the continents, but geodesists are able to derive the heights of continental points above this imaginary, yet physically defined, surface by a technique called spirit leveling.

Being an equipotential surface, the geoid is by definition a surface to which the force of gravity is everywhere perpendicular. This means that when travelling by ship, one does not notice the undulations of the geoid; the local vertical (plumb line) is always perpendicular to the geoid and the local horizon tangential to it. Likewise, spirit levels will always be parallel to the geoid.

Note that a GPS receiver on a ship may, during the course of a long voyage, indicate height variations, even though the ship will always be at sea level (tides not considered). This is because GPS satellites, orbiting about the center of gravity of the Earth, can only measure heights relative to a geocentric reference ellipsoid. To obtain one's geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in traditional land surveying, will always be geoidal height. Modern GPS receivers have a grid implemented inside where they obtain the geoid (for e.g. EGM-96) height over the WGS ellipsoid from the current position. Then they are able to correct the height above WGS ellipsoid to the height above WGS84 geoid. In that case when the height is not zero on a ship it is because of the tides.

Spherical harmonics representation

Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96 (Earth Gravity Model 1996), determined in an international collaborative project led by NIMA. The mathematical description of the non-rotating part of the potential function in this model is

:$V=\backslash frac\{GM\}\{r\}\backslash left(1+\{\backslash sum\_\{n=2\}^\{n\_\{max\}\}\}\backslash left(\backslash frac\{a\}\{r\}\backslash right)^n\{\backslash sum\_\{m=0\}^n\}\; \backslash overline\{P\}\_\{nm\}(\backslash sin\backslash phi)\backslash left[\backslash overline\{C\}\_\{nm\}\backslash cos\; m\backslash lambda+\backslash overline\{S\}\_\{nm\}\backslash sin\; m\backslash lambda\backslash right]\backslash right),$ .]]

where $\backslash phi\backslash$ and $\backslash lambda\backslash$ are geocentric (spherical) latitude and longitude respectively, $\backslash overline\{P\}\_\{nm\}$ are the fully normalized associated Legendre polynomials of degree $n\backslash$ and order $m\backslash$, and $\backslash overline\{C\}\_\{nm\}$ and $\backslash overline\{S\}\_\{nm\}$ are the numerical coefficients of the model based on measured data. Note that the above equation describes the Earth's gravitational potential $V\backslash$, not the geoid itself, at location $\backslash phi,\backslash ;\backslash lambda,\backslash ;r,\backslash$ the co-ordinate $r\backslash$ being the geocentric radius, i.e., distance from the Earth's centre. The geoid is a particular equipotential surface, and is somewhat involved to compute. The gradient of this potential also provides a model of the gravitational acceleration. EGM96 contains a full set of coefficients to degree and order 360 (i.e. $n\_\{max\}\; =\; 360$) , describing details in the global geoid as small as 55 km (or 110 km, depending on your definition of resolution). The number of coefficients, $\backslash overline\{C\}\_\{nm\}$ and $\backslash overline\{S\}\_\{nm\}$, can be determined by first observing in the equation for V that for a specific value of n there are two coefficients for every value of m except for m = 0. There is only one coefficient when m=0 since $\backslash \; sin\; (0\backslash lambda)\; =\; 0$. There are thus (2n+1) coefficients for every value of n. Using these facts and the well known formula, $\backslash sum\_\{I=1\}^\{L\}I\; =\; L(L+1)/2$, it follows that the total number of coefficients is given by

:$\backslash sum\_\{n=2\}^\{n\_\{max\}\}(2n+1)\; =\; n\_\{max\}(n\_\{max\}+1)\; +\; n\_\{max\}\; -\; 3\; =\; 130317$ using the EGM96 value of $\backslash \; n\_\{max\}\; =\; 360$ .

For many applications the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms.

New even higher resolution models are currently under development. For example, many of the authors of EGM96 are working on an updated model that should incorporate much of the new satellite gravity data (see, e.g., GRACE), and should support up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients). NGA has announced the availability of EGM2008, complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159. Software and data is on the Earth Gravitational Model 2008 (EGM2008) - WGS 84 Version page.

Precise geoid

The 1990s saw important discoveries in theory of geoid computation. The Precise Geoid Solution by Vaníček and co-workers improved on the Stokesian approach to geoid computation. Their solution enables millimetre-to-centimetre accuracy in geoid computation, an order-of-magnitude improvement from previous classical solutions.

Time-variability

Recent satellite missions, such as GOCE and GRACE, have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June, 2010, through the European Space Agency (ESA)’s Earth observation user services tools. ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles, mass balances of ice sheets, and postglacial rebound. From postglacial rebound measurements, time-variable GRACE data can be used to deduce the viscosity of Earth's mantle.

References

External links

Main NGA (was NIMA) page on Earth gravity models

EGM96 NASA GSFC Earth gravity model

Earth Gravitational Model 2008 (EGM2008, Released in July 2008)

NOAA Geoid webpage

GeographicLib provides a utility GeoidEval (with source code) to evaluate the geoid height for the EGM84, EGM96, and EGM2008 earth gravity models. Here is an online version of GeoidEval.

Kiamehr's Geoid Home Page

Geoid tutorial from Li and Gotze (964KB pdf file)

Geoid tutorial at GRACE website

Precise Geoid Determination Based on the Least-Squares Modification of Stokes’ Formula(PhD Thesis PDF)

See also

Physical geodesy

Geodesy

Category:Gravimetry Category:Gravitation

Caption	President of IRF
Birth name	Zakir Abdul Karim Naik
Birth date	October 18, 1965
Birth place	Mumbai, Maharashtra, India
Education	Kishinchand Chellaram College
Alma mater	University of Mumbai
Occupation	President of Islamic Research Foundation, Orator, Public speaker
Years active	1991–present
Boards	Islamic Research Foundation
Religion	Islam
Influenced by	Ahmed Deedat
Spouse	Farhat Zakir Naik
Website	IRF.net PeaceTV

Zakir Abdul Karim Naik (Urdu: ذاکر عبدالکریم نائیک; born 18 October 1965) is the founder and president of the Islamic Research Foundation (IRF), which is a non-profit organization that owns Peace TV channel based in Mumbai, India. A prominent Muslim figure in the Muslim world, Naik is also a public speaker and a writer on the subject of Islam and other comparative religion.

Naik originally began his career as a medical doctor, having attained a Bachelor of Medicine and Surgery (MBBS) from the University of Mumbai. After being inspired by Ahmed Deedat, Naik began part-time and later switching to a full-time career by giving Islamic speeches to the public.

Biography

Zakir Abdul Karim Naik was born on 18 October 1965 in Mumbai, India. He attended St. Peter's High School (ICSE) in the city of Mumbai. Later he joined the Kishinchand Chellaram College and then studied medicine at Topiwala National Medical College and Nair Hospital in his native city and received his MBBS degree from the University of Mumbai. In 1991 he started working in the field of Da'wah Islam.

Naik says he was inspired by the late Ahmed Deedat, who had been active in the field of Da'wah for more than 50 years. According to Naik, his goal is to "concentrate on the educated Muslim youth who have become apologetic about their own religion and have started to feel the religion is outdated", He considers it a duty of every Muslim to remove perceived misconceptions about Islam, to counter what he views as the Western media's anti-Islamic bias in the aftermath of September 11, 2001 terrorist attacks upon the United States. Some of his articles are also published in magazines like the Islamic Voice.

Anthropologist Thomas Blom Hansen has written Topics he speaks on include: "Islam and Modern Science", "Islam and Christianity", and "Islam and secularism".

Apart from IRF, Naik is also the founder and chairman of the Islamic International School (IIS), Mumbai. He is also the founder of Peace TV Network.

Lectures and debates

Naik has held many debates and lectures around the world as well as in Mumbai, India. One of Naik's most cited debates took place in Chicago in April, 2000 featuring William Campbell of Pennsylvania, USA on the topic "The Qur'an and the Bible: In the Light of Science".

Naik also stated that "despite the strident anti-Islam campaign, 34,000 Americans have embraced Islam from September 2001 to July 2002." He cited an article by Edward Said published in the Time magazine, which said that 60,000 books about Islam and the Orient have been written between 1800 and 1950 alone.

In a lecture at Melbourne University, Naik argued that only Islam gave women true equality. He stressed the importance of the headscarf by arguing that the more "revealing Western dress" makes women more susceptible to rape.

On 21 January 2006, Naik held an inter-religious dialogue with Sri Sri Ravi Shankar. The event was about the concept of God in Islam and Hinduism, the aim being to bring understanding between the two major religions of India, and at best to point out the commonalities between them. It was held in Bangalore, India with up to 50,000 attending at the Palace Grounds.

In a lecture delivered on 31 July 2008 on Peace TV, Naik stated, regarding 9/11: "it is a blatant, open secret that this attack on the Twin Towers was done by George Bush himself", to give Bush reason to attack and control oil-rich countries.

On 7 March 2010 Naik participated in a live discussion with Soha Ali Khan and others on a TV show We The People on NDTV.

Peace conferences

Every year since November 2007, Naik has lead a 10-day "Peace Conference" at Somaiya Ground, Sion, Mumbai. Lectures on Islam have been presented by Naik as well as twenty other Islamic scholars from around the world. Another prominent personality was the Malaysian politician, Anwar Ibrahim in 2008.

During one of the lectures at the Peace Conference, Naik provoked anger among members of the Shia and Sunni communities, when he mentioned the words "Radiallah ta'la anho" (meaning 'May Allah be pleased with him') after mentioning the name of Yazid I and made remarks that the battle of Karbala was political. Others, however, believed the comment was blown out of proportion.

In November 2009, the IRF organized a 10-day international Islamic conference and exhibition titled 'Peace – the solution for humanity' at the Somaiya grounds in Mumbai. Lectures on Islam were presented by Naik as well as thirty other Islamic scholars from around the world.

Writings

In 2007, the Saudi publishing house, Dar-us-Salam Publications, published two titles written by Naik, entitled "The Concept of God in Major Religions" and "The Qur'an and Modern Science: Compatible or Incompatible?".

Criticism and controversy

On the issue of the theory of evolution, Naik commented that it contradicts Islam since it remains "just a theory and not a fact". According to Naik, scientists "support the theory, because it went against the Bible – not because it was true." According to Naik, there are hundreds of scientists and Nobel Prize winners who speak against Darwin's theory.

In 2004, Naik visited New Zealand and then the Australian capital at the invitation of Islamic Information and Services Network of Australasia. At his conference in Melbourne, senior Age writer and columnist Sushi Das commented that "Naik extolled the moral and spiritual superiority of Islam and lampooned other faiths and the West in general", further criticizing that Naik's words "fostered a spirit of separateness and reinforced prejudice".

In August 2006, Naik's visit and conference in Cardiff (UK) were the object of controversy, when Welsh MP David Davies called for his appearance to be cancelled. He argued that Naik was a 'hate-monger', and said his views did not deserve a 'public platform'; Muslims from Cardiff, however, defended Naik's right to speak in their city. Saleem Kidwai, Secretary General of the Muslim Council of Wales, disagreed with Davies, stating that "people who know about him (Naik) know that he is one of the most uncontroversial persons you could find. He talks about the similarities between religions, and how should we work on the common ground between them", whilst also inviting Davies to discuss further with Naik personally in the conference. The conference went ahead, after the Cardiff council stated it was satisfied that he would not be preaching extremist views. Khushwant Singh, a prominent Indian journalist, politician and author argues that Naik's pronouncements are "juvenile" and said that "they seldom rise above the level of undergraduate college debates, where contestants vie with each other to score brownie points". Singh disagreed with Naik's statement that "Western society claims to have uplifted women. On the contrary, it has actually degraded them to the status of concubines, mistresses, and society butterflies who are mere tools in the hands of pleasure seekers and sex marketers". Singh wrote: "Dr. Naik, you know next to nothing about the Western society and are talking through your skull cap. People like you are making the Muslims lag behind other communities." Singh also noted that Naik's audiences "listen to him with rapt attention and often explode in enthusiastic applause when he rubbishes other religious texts".

Fatwas

In August 2008, Darul Uloom Deoband issued a fatwa stating: "The statements made by Dr Zakir Naik indicate that he is a preacher of Ghair Muqallidin. One should not rely upon his speeches.".

The Shariah Board of America has also issued more than 20 fatwas against Naik on their website. They believe Naik has gone astray, as he is not a scholar and issues Islamic teachings without authority or any knowledge to do so, which is dangerous to Islam; "Naik is known for discussions on comparative religions. He is not a qualified Aalim of deen. His comments on fiqh have no merit. If it is true that he condemned the fiqh of the Imams, then that in itself is a clear indication of his lack of fiqh and understanding of Shariah. We have come across a fatwa from Darul Ifta Jamia Binnoria, Pakistan regarding Zakir Naik not being a certified Aalim of Deen. He should consult with Ulama in his endeavor of propagating deen."

In November 2008 the Lucknow-based cleric Abul Irfan Mian Firangi Mahali issued a fatwa against Naik, describing Naik as a "Kafir" (non-believer) and stating in the fatwa, that Naik should be ex-communicated from Islam. He argued that "Naik is not an Islamic scholar. His teachings are against the Quran. In his speeches, he insults Allah and glorifies Yazeed, the killer of Imam Hussain", and that Naik had supported Osama bin Laden and called upon all Muslims to become terrorists. Naik, however, said that his speeches had been misquoted and that he was allegedly targeted by people with vested interests and said of the fatwa: "fatwas mean nothing. They should also issue fatwas against Imam Bukhari. Some clerics who have limited understanding of Islam are doing these things. It doesn't affect me". The All-India Sunni Board and Sheikh Abdul Qadir Jilani Foundation have also defended Naik.

Views on apostasy

Naik has stated that any Muslim is free to convert out of Islam if the person so chooses, but added that if a Muslim converts and then speaks against Islam it should be considered as treason. Naik stated that under Islamic law this is punishable by death.

During a question and answer session at Naik's lecture on May 29 on the Maldives, a 37-year old Maldivian citizen named Mohamed Nazim stood up and announced that he was struggling to believe in any religion and did not consider himself to be a Muslim. Nazim further asked what Naik's verdict would be under Islam and in the Maldives. Dr Naik responded that he considers the punishment for apostasy does not necessarily mean death, since Muhammed was reported in the Hadith scriptures on some occasion to have shown clemency towards apostates, but added that if a Muslim apostate speaks and propagates against Islam under Islamic Shari’a rule then the apostate should be put to death.

Views on homosexuality

During a 16 October, 2006 lecture, Naik said that "one-third of New York are gays" and that homosexuality is "a problem" in the United States.

Views on terrorism

Naik's views and statements on terrorism have at times been criticised in the media and by the United Kingdom Home Secretary. In a YouTube video speaking of Osama bin Laden, Naik said that he would not criticise bin Laden because he had not met him and did not know him personally. He added: "If he is fighting the enemies of Islam, I am for him. If he is terrorizing the terrorists, America, the biggest terrorist, I am with him. Every Muslim should be a terrorist. ... A terrorist is a person who causes terror. The moment a robber sees a policeman he is terrified. A policeman is a terrorist for the robber. Similarly every Muslim should be a terrorist for the antisocial elements of society, such as thieves, dacoits and rapists. Whenever such an anti-social element sees a Muslim, he should be terrified. It is true that the word ‘terrorist’ is generally used for a person who causes terror among the common people. But a true Muslim should only be a terrorist to selective people i.e. anti-social elements, and not to the common innocent people. In fact a Muslim should be a source of peace for innocent people." This evoked strong criticism from Hindus in general and Arya Samaj in particular, who consider Vedas to be revealed texts. Because Naik claimed to have defeated Sri Sri Ravi Shankar in a debate, he was challenged to debate Arya Samaj on this issue. After he refused to officially respond, a detailed rebuttal of Naik's views along with the details of communications with IRF was made online by Arya Samaj.

2010 exclusion from the UK and Canada

Naik has been denied entry into the United Kingdom and Canada since June 2010. He was banned by the Home Secretary Theresa May. He had arranged to give talks in London and Sheffield. May said of the exclusion order regarding Naik, "Numerous comments made by Dr Naik are evidence to me of his unacceptable behavior". She noted statements from Naik such as, "every Muslim should be a terrorist". Naik's full quote is: "Every Muslim should be a terrorist. A terrorist is a person who causes terror. The moment a robber sees a policeman he is terrified. A policeman is a terrorist for the robber. Similarly every Muslim should be a terrorist for the antisocial elements of society, such as thieves, dacoits and rapists".

Naik believed that the Home secretary was making a "political decision and not a legal one". It was reported that Naik would attempt to challenge the ruling in the High court. His application for judicial review was dismissed on 5 November 2010.

Influence as revealed by published newspaper rankings

On 31 January 2010, the Sunday Express published The Indian Express list of the “100 Most Powerful Indians in 2010”. It ranked Naik at 89. Of the Muslims in this list, Naik was the only Islamic preacher. The other Muslims were a political secretary, a politician, a government official, a business magnate and three film personalities. He was the third most influential religious figure listed in 2009, whereas in 2010 he rose to become the highest placed religious leader at No. 89 followed by Jaggi Vasudev at 94, Baba Ramdev at 99 and Sri Sri Ravi Shankar at 100.

References

External links

Islamic Research Foundation (official website)

Peace TV (official website)

Articles and Answers of Zakir Naik

Here’s Zakir Naik, ‘Fundamentalist, not Fanatic’ Mumbai Newsline

Correct Islamic Faith International Association

Second opinion: Zakir Naik’s ‘reverse orientalism’ —Khaled Ahmed’s TV Review

Response of Arya Samaj to Zakir Naik's views on Hinduism

Official Peace Conference Website

Zakir Naik Exlusion Official Website

Category:1965 births Category:Living people Category:Muslim scholars Category:Indian Muslims Category:Muslim apologists Category:Konkani Muslims Category:People from Mumbai Category:Indian religious leaders Category:University of Mumbai alumni Category:Personae non gratae