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greenwich meantime naviagation

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Astro Navigation Demystified
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Converting GMT to GHA

Greenwich Mean Time (GMT) is the local mean time anywhere on the meridian of Greenwich. In other words it is the Local Hour Angle of the Mean Sun on the meridian of Greenwich.

Since the Greenwich meridian is used as the base meridian from which the longitude of all places on Earth are identified, it provides the link between the LMT of a place and the LMT at Greenwich (or GMT).

Example. In the diagram below, imagine that we are looking down on the North Pole.

GMT white

P represents the North Pole

G represents the position of Greenwich on the Earth’s surface.

GP represents part of the Greenwich Meridian (0o).

MP represents part of the meridian of longitude 45oW and M is a point on that meridian.

AP represents part of the meridian of longitude 30o E and A is a point on that

meridian.

The meridian of the Mean Sun, for a very brief instant, coincides with the meridian 45oW. and so, at that instant, the Local Mean Time at point M is noon.

At the same instant, the Local Hour Angle of the Mean Sun at Greenwich is 45o. Therefore, the LMT at Greenwich must be 3p.m. since the time difference for 45o is 3 hours and Greenwich is to the East of M.

It follows that the Greenwich Mean Time must also be 3p.m. (since GMT is equal to the LMT at Greenwich).

The LMT at point A must be 2 hours after GMT (since the time difference for 30o is 2 hours and A is to the East of Greenwich).

Therefore, the LMT at point A must be 5p.m.

Greenwich Hour Angle (GHA). The angle between two meridians of Longitude can be expressed as an hour angle. The hour angle between the Greenwich Meridian and the meridian of a celestial body is known as the Greenwich Hour Angle.

The Local Hour Angle between an observer’s position and the geographical position of a celestial body can be found by combining the observer’s longitude with the GHA.

In the diagram below , O represents the longitude of an observer;

X represents the meridian of a celestial body;

G represents the Greenwich Meridian.

diag 5 nonumBecause in this case, the observer’s longitude is east and because LHA is measured westwards from the observer’s meridian to the meridian of the celestial body, LHA is equal to the longitude plus the GHA.

For a fuller explanation of GHA and LHA click here

Converting GMT to GHA.

Because GMT is measured westwards from the reciprocal of Greenwich (i.e. 180o) and GHA is measured westwards from the Greenwich meridian (i.e. 0o) we convert GMT to GHA as follows: If GMT, when converted to arc, is less than 180o then add 180o; if GMT is greater than 180o then subtract 180o). Examples:

Example 1. Convert 0840 GMT to GHA.

Step 1. Convert GMT to arc.

8h = 8 x 15 = 120o 0’ 0”

40m = 40 ÷ 4 = 10o 0’ 0”

= 130o 0’ 0”

Step 2. Convert to GHA.

GHA =130o 0’ 0” + 180o 0’ 0” = 310o 0’ 0”

Example 2. Convert 1530 GMT to GHA.

Step 1. Convert GMT to arc.

15h = 15 x 15 = 225o 0’ 0”

30m = 30 ÷ 4 = 7o 30’ 0”

= 232o 30’ 0”

Step 2. Convert to GHA.

GHA = 232o 30’ 0” – 180o 0’ 0” = 52o 30’ 0”

Note. Because GHA relates to apparent solar time and GMT relates to mean solar time, we must take the equation of time (EOT) into account when converting GMT to GHA. Therefore the next example includes a calculation for EOT.

Example 3. Convert 0415 GMT to GHA. E0T = +1 m

Equation of Time = mean solar time – apparent solar time

∴ apparent solar time = mean solar time – equation of time

∴ GHA = GMT – EOT.

Step 1. Convert 0415 GMT to arc.

4h = 4 x 15 = 60o 0’ 0”

15m = 15 ÷ 4 = 3o 45’ 0”

= 63o 45’ 0”

– EOT – 1’ 0” (correction for EOT)

= 63o 44’ 0”

Step 2. Convert to GHA.

GHA =63o 44’ 0” + 180o 0’ 0’’ = 243o 44’ 0”

Latitude & Longitude & GreenWich MeanTime Navigation

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How do I determine my longitude and latitude without any technology?
You can do it with:
A quadrant,
A Sundial
A Watch

The first part is the easiest – latitude
At sea, in the middle of nowhere, to find out your latitude, you find Polaris.
Polaris is a star that is exactly aligned with the axis of the Earth toward the north. No matter where you are in the northern hemisphere this star is toward the North.

Polaris is in the axis of the Planet Earth

And therefore always at the same place in the sky, regardless of earth rotation.

Now, given the location of Polaris, if you are navigating in the northern hemisphere, it will be above your head if you are at the north pole (90°) and right on the horizon (0°) if you are on the equator, any position. You then use a quadrant to measure as accurately as possible the position of Polaris above the horizon, and this is you Latitude.
If you are in the southern hemisphere your could use Sigma Octantis instead but it is much more difficult and not as accurate.
If this is during the day you can find out using the sun. Now this is more difficult. But the sun at 12:00 on 20th March / September(equinox) will be right above your head on the equator and will be at the horizon on the north pole. You use your quadrant again to measure the angle and your latitude is 90- your results….
Now to measure your longitude. Well sorry but you cannot do it without a great piece of technology. It took about 60 years to be created from the moment the British government offered £20 000 to whomever could make it.
This my friend, is a watch. Not a simple one, oh no. A watch that gives Greenwich time for months without running fast or slow EVEN ON A BOAT. Because of course the mechanism of any watch from the 18 century would struggle with the movements of a boat.
The principle is easy, once we have defined that the line going through Greenwich observatory is the mark 0 (which in itself wasn’t that simple as Paris was claiming it as well). Your longitude is the time difference between Greenwich and your position (between 0 and 24 hours) translate into degrees (0 – 360).

So what you need is to know the time wherever your are and then the time in London.
If you think the former is the most difficult … think again.
With a sundial, it is fairly straightforward to know the time.
To know the time in Greenwich, however you need to have embarked a watch showing the time there and that hasn’t been impacted by the movement of the boat at sea.
So now that you have the time difference between your place and Greenwich you know how far you went.

Mahalo

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I founded www.adapt.org in 1980 it now has over 50 million members.
$500 of material=World’s fastest hydrofoil sailboat. http://sunrun.biz

AmericanTech

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I founded www.adapt.org in 1980 it now has over 50 million members.
$500 of material=World’s fastest hydrofoil sailboat. http://sunrun.biz

8most famous supreme Court cases

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The Supreme Court of the United States handles the most important court cases in our country, so famous Supreme Court decisions have helped shape our country’s history. The Court has tremendous powers to impact laws that everyday citizens will abide by for years to come. And while most of these decisions didn’t involve any use of legal document solutions or docketing software, these 8 decisions (and a bonus) have impacted the history of the United States. That’s why it’s valuable to learn about and from landmark Supreme Court cases that changed the way Americans live. Let’s take a look at a few of these important and interesting Supreme Court cases.

Marbury v. Madison, 1803

Long before there were mobile apps for lawyers, Marbury v. Madison was one of the most important Supreme Court cases because it established the Supreme Court’s power of judicial review (the right to declare a law unconstitutional) over Congress. It also helped define the boundary between the executive and judicial branches of the United States government.

McCulloch v. Maryland, 1819

McCulloch v. Maryland is one of the more famous Supreme Court cases because it established the federal government’s implied powers over states. The Supreme Court made the decision when the state of Maryland began imposing a tax on all bank notes not chartered by Maryland. Because the Second Bank of the United States was the only out-of-state bank existing in Maryland at the time, it was interpreted as an attack on the federal bank. Therefore, the tax law was ruled unconstitutional because it was an attempt to violate the powers of the federal government in one of the Supreme Court’s earlier landmark cases.

Gideon v. Wainwright, 1963

list of famous court cases must include Gideon v. Wainwright because it established the right of a criminal defendant to have an attorney even if they could not personally afford to pay for one. In this famous Supreme Court case, the Court unanimously ruled that due to the Fifth and Sixth Amendment to the U.S. Constitution, states are required to provide an attorney to defendants who cannot afford to pay for one.
The case involved a burglary where the person charged was denied the right to an attorney just because they couldn’t afford to pay for one. After being charged with the crime of burglary, Gideon (the person charged) arrived at the courthouse too poor to pay for counsel. Here’s what happened:

The case involved a burglary where the person charged was denied the right to an attorney just because they couldn’t afford to pay for one. After being charged with the crime of burglary, Gideon (the person charged) arrived at the courthouse too poor to pay for counsel. Here’s what happened:

The COURT: Mr. Gideon, I am sorry, but I cannot appoint counsel to represent you in this case. Under the laws of the State of Florida, the only time the court can appoint counsel to represent a defendant is when that person is charged with a capital offense. I am sorry, but I will have to deny your request to appoint counsel to defend you in this case.

GIDEON: The United States Supreme Court says I am entitled to be represented by counsel.

The Florida court declined to appoint counsel for Gideon. As a result, he was forced to act as his own counsel and conduct his own defense in court, emphasizing his innocence in the case. At the conclusion of the trial, the jury returned a guilty verdict. The court sentenced Gideon to serve five years in the state prison.

After being convicted, Gideon appealed to the United States Supreme Court that his Sixth Amendment rights had been violated. Eventually, the Supreme Court ruled that counsel must be provided to defendants who can’t afford an attorney, and, as a result of that ruling, over 2,000 previously convicted people were released from Florida’s prisons. Today, indigent prisoners are appointed lawyers so that they can get a fair trial in court.

Miranda v. Arizona, 1966

Miranda v. Arizona was an important and landmark Supreme Court case that established the requirement that police advise people in custody of their rights before questioning them. This important Supreme Court case has had a significant impact on how American law enforcement operates. What is now known as Miranda rights are an essential part of police procedure in every state and city/town. This was a very controversial Supreme Court case at the time, as the court was split (5-4).

Loving v. Virginia, 1967 (9-0 decision)

Loving v. Virginia didn’t involve family lawyer software but was definitely considered one of the landmark court cases, as it invalidated laws forbidding interracial marriage. The case was brought by Mildred Loving (a black woman) and Richard Loving (a white man) who were sentenced to one year in prison for marrying each other, which was against the law in Virginia. The state of Virginia had a “Racial Integrity” law that prohibited marriages between whites and blacks. This famous Supreme Court case found these “anti-miscegenation” laws to be unconstitutional.

Roe v. Wade, 1973

Roe v. Wade might be one of the most famous and controversial U.S. Supreme Court cases in history, with its ruling permeating our U.S. politics to this day. Roe v. Wade determined that the right to privacy under the Due Process Clause of the Fourteenth Amendment extended to a woman’s decision to have an abortion. The controversial Supreme Court case also established that the right of woman to have an abortion was limited to the third trimester of pregnancy. But in the subsequent Supreme Court case of Planned Parenthood v. Casey (1992), the Court determined that a woman has a right to abortion until fetal viability–the ability of the fetus to live outside the woman’s body. Considered one of the more controversial Supreme Court cases, Roe v. Wade struck down many abortion restrictions created by states. New restrictions have arisen since, and the right to abortion has been consistently challenged by opponents since 1973.

United States v. Nixon, 1974

United States v. Nixon is also on our list of 8 of the most important Supreme Court cases. It prohibited sitting Presidents from using their executive powers to withhold evidence during a criminal investigation. The Supreme Court ruled that the U.S. President could not claim executive privilege to withhold evidence being requested by a court during a criminal investigation. In the case, President Nixon was embroiled in the Watergate scandal and was facing impeachment. A lower court requested copies of tapes that they determined included incriminating evidence against people under investigation and possibly the president himself. When President Nixon refused to deliver the tapes, the Supreme Court ruled that he had no rights to invoke his executive privilege in a criminal case.

Obergefell v. Hodges, 2015

Obergefell v. Hodges was a landmark Supreme Court case that held same-sex couples had a fundamental right to marry as guaranteed by the Due Process Clause and the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution. The famous Supreme Court case made it possible for same-sex couples to get married in all fifty states, and the ruling required all fifty states to lawfully perform and recognize same-sex marriages on the same terms and conditions as opposite-sex marriages. This important case has been challenged by some states, but the Supreme Court has ruled that bans on same-sex marriages are unconstitutional.

BONUS: Brown v. Board of Education of Topeka, 1954

Since our first release of this list of the most famous and controversial Supreme Court cases, we wanted to include one more that had a tremendous impact on society and our education system. Brown v. Board of Education is easily one of the most famous cases in our nation’s history. In it, the Supreme Court held that “separate but equal” had no place in public education. The Court effectively ended segregation in public schools saying that separate educational institutions provided inherently unequal educations for white and black students to the detriment of black students. To the Court, those black students were deprived of equal protection guaranteed by the Fourteenth Amendment of the U.S. Consitution.

The Supreme Court continues to have a powerful influence on how laws are interpreted today. And Smokeball law firm practice management software can have a powerful influence on how you manage and run your practice. Sign up for your free demo and see why the most successful small law firms use Smokeball!

as a Senior Editor of the Wash. U. Law Review, held the prestigious Thompson Coburn Research Fellowship, served as Research Assistant to then-Vice-Dean (now Chancellor) Andrew D. Martin, and clerked at the U.S. District Court for the Eastern District of Missouri. He holds a B.A. in Political Science and a B.M. in Music Performance with Honors Scholar distinction from the University of Connecticut, making him a Huskies basketball fan through and through. Follow Josh’s activity on LinkedIn, and keep up with new articles on the Smokeball Blog.
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