Answer to the Question 02/00
HALLEY'S PLANETThe question was:
Not so many years ago there was no order of magnitude estimate of the age of the planet Earth. Edmund Halley (yes, that's the "comet guy") wrote an article in Philosophical Transactions of the Royal Society of London, 29, 296 (1714), where he observed that lakes that emit no rivers (such as Dead Sea, or Caspian Sea) are very salty, and thus it is reasonable to assume that rivers bring salt into the lakes. He further claimed that "'tis not improbable that the ocean it self is become salt from the same cause." Consequently, by measuring the salinity of the oceans and by determining the amount of salt brought by rivers every year, one could estimate the age of the Earth. Halley lacked the data to actually perform an estimate of the age of the Earth using his method. Halley's assumptions are wrong, but nevertheless it was a nice try for his time. What would be the age of Earth according to Halley's method?
(11/2000) Y. Kantor: The problem was solved (9/2000) by Marakani Srikant from the National University of Singapore (e-mail srikant@s130119.pc.nus.edu.sg). He suggested a nice "back of the envelope" solution. (E.g., he estimated the total river discharge as 5 times Amazon river, etc. While some of his numbers were by an order of magnitude off the target, the final answer is rather close to what we present below.)
Answer: About 40 million years.
Solution:
The total amount of water in the oceans is 1.37 109 km3.
The total river inflow per year is 37,300 km3.
1 kilogram of sea water contains 10 grams of Na+ ions, or 35 grams of salts (mostly sodium and magnesium chlorides) per kilogram of water.
It is difficult to define what exactly is called "fresh water" and what is the mean salinity of rivers. A nice reference on salinity is here. It says that there is about factor 1000 between salinity of soft river water and the sea.
From this data we deduce that "the age of the earth" is 1.37 109 km3/37,300 * 1000=4 107years. Not bad for an estimate of geological time, although we are more than two orders magnitude off. Now, can you tell the reasons for this number being such a strong underestimate of an actual answer?
(12/2000) Paul N. Taylor from Oxford, England (e-mail royatluap@aol.com) sent us the following e-mail regarding the question asked above:
In the answer to the problem of the age of the earth from the salt in the sea you pose the supplementary question of why that method produces such an underestimate for the age of the Earth. The key to the problem is that the ocean basins constitute a rather leaky container. The rivers go on and on feeding salt into the system, but it is perhaps not quite so clear how the salt is then taken out of the ocean water system.
Over the last few decades our understanding of the workings of the oceans have been greatly enhanced by the development of the theory of plate tectonics and sea floor spreading. New ocean floor is being created at the mid-ocean ridges by the frequent eruption of basaltic lavas (MORB: Mid Ocean Ridge Basalts). When freshly erupted, these basalts have a rather low sodium concentration. However, another very important process taking place at and near the mid-ocean ridges is the hydrothermal interaction of seawater with the newly erupted lavas. In this process massive volumes of ocean water are processed through the basalt lava piles in convection cells which penetrate deep into the lava pile. The seawater is strongly heated by this process and very extensive chemical exchanges take place between the seawater and the basalts. The composition of hydrothermally altered basalts typically show sodium concentrations greatly increased relative to fresh MORB. The fate of most of this highly modified basalt, on a timescale of ca. 200 Million Years is to be transported away from the mid-ocean ridge by the "conveyor belt" process of sea-floor spreading eventually to be consumed back into the mantle at a subduction zone. Much of the sodium and the water loaded onto the "conveyor belt" by the hydrothermal activity at the ridge is probably released from the descending subducted slab as it warms up, and these materials contribute significantly to a second round of volcanic activity in the island arcs or Andean-type volcanic chains which presently surround the Pacific [the oldest of the Earth's present oceans]. These issues are all dealt with very effectively in most of the modern textbooks of Igneous Petrology or Plate Tectonics.
The "age of the Earth" by the salt in the sea method has found important applications in modern geochemistry. The "age" given by this method is now understood better in terms of a residence time in the ocean water mass for each chemical species - given by (the mass of the species in the ocean water mass)/(the rate of supply of the species to the ocean mass). The matter is dealt with in "Inorganic Geochemistry" by Paul Henderson, Pergamon 1982; and also in "The Continental Crust: its composition and evolution" by SR Taylor & SM McClennan, Blackwell 1985.
p.s. It appears that creationists just love this way of measuring age of earth, since it ensures "young" earth (maybe not young enough for their taste, but "it's at least something"). If you want to have some "creationist fun" take a look at the Answers in Genesis. (We thank Ido Golding from Tel Aviv University for this reference.)
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