usually we unroll a ribbon to find the length but we cannot physic-ly measure to the sun and we can barely go and measure 8 kilometers up a tall mountain so we can use the triangle formulas.
if we know the distance to the moon at the time when the moon is "right angle 90 degrees" from our planet earth then that is the base of a right triangle so if we know two angles and the length of the base we can calculate the length with triangle formula.
to know the distance to the sun first we must find a right angle. we see the moon changes in cycles from full disk bright to less and return to full disk. when the moon is half bright we know that we are aligned so the sunlight hits the face of the moon and we see from the side so that is 90 degrees called right triangle the we can calculate with sin or cosin or tangent.
next for finding the distance to sun we need the length to the moon which they found. over 2000 years ago hipparchus found the length around year 150 bc. story: "observing the Moon from two cities a known distance apart, Hipparchus used a little geometry to compute its distance to within 7% of today’s modern value " first he used this triangular method to measure the angle of the triangle to the moon with length between two cities. the distance to moon averages to around 384.4 thousand kilometers or 384.4 million meters known from the two cities and angles. that side of triangle called base of the triangle together with the two angles: angle a= 90 degrees when we face side of moon half bright with the angular degrees of the second angle 89.8 degrees almost 90, [they estimated 87 degrees in ancient times pretty close], indicates far.
another story following the instructions of halley [edmund lived around 1700] he predicted when venus would pass between earth and sun and how to compute and they did hence discovering "French astronomer Jerome Lalande collected all the data and computed the first accurate distance to the Sun: 153 million kilometers, good to within three percent of the true value" but a bit more than the distance we know now,
knowing the two angles of the triangle 90 [from side called right angle] and 89.8 we can calculate the length of the sides "Side a = 384 units therefore: Side b = 110,007.4 and Side c = 110,008.1" very far 110 million kilometers. good estimate but using halley calculation was more precise and we discovered even further from sun.
now the idea of meter itself is troublesome but once we know 110 million kilometer and 153 million kilometer and 149.6 million kilometer we can estimate based on the speed of light that light needs eight minutes and nineteen seconds to reach earth from the sun. As of 2012, 1 AU = 149,597,870,700 meters exactly. so 149.6m.km.
we call that one unit and we can use that to say that planets nearer to the sun than us, are less than one a.u. while the further ones are more than one au.
list: from sun to each planet, in AU.
Mercury: 0.387 AU
Venus: 0.723 AU
Earth: 1.000 AU=one astronomical unit (AU) = 92,955,807 miles (149,597,871 km). since 149,597,870,700 meters at speed 299,792,458 meters each second, 499 seconds 19 seconds more than 8 minutes so around 500 light-seconds away.
Mars: 1.524 AU
Jupiter: 5.203 AU
Saturn: 9.582 AU
Uranus: 19.201 AU
Neptune: 30.047 AU
in summary mercury is nearly one third between e and sun. but venus is 2/3.
saturn is twice as far from earth as jupiter and u is twice as far from e as saturn.
saturn is around midway between e and u. and jupiter is around midway between e and s.
the Earth’s orbit isn’t perfectly round, we actually get about 3% closer and farther throughout the course of a year.
now that we built the system on the flawed foundation of meters and translated it to a.u. we can say why meter is bad.
the system of kilometer and centimeter is based on meters and ten which has a flaw we can only divide evenly in 2 or 5 but not 3 or 4 the whole reason we divided the day into 24 hours is to allow thirds in even parts and sam divided the year cycle as defined astronomicly into twelve months so we have even thirds. but a third of a meter is a problem and then "rounding" to the nearest meter is inaccurate.
also the decision that a certain length is called a meter iis stupid. what did they do? they calculated the circumference of the earth and cut it into millions of peices. why is that better than anything else? keep the traditional kings shoe. in fact the same shoe could be worn by many kings if the shoe is big enough and padding is inserted ! so better to use the "foot" of the king as measured in the "universal king shoe" which the king long ago put one and that "foot" can be divided into twelve inches the same system as twelve month division of the year.
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