How Accurate Is Our Estimation of the World’s Ocean Mass?

In summary, the estimated mass of water in all the World's oceans is about 2.1*1021 kg, based on the assumption that the Earth's crust is a spherical shell and using the average depth of the oceans and the surface area of the Earth. This calculation may be improved by using more accurate values for the radius and density of seawater.
  • #1
hasan_researc
170
0

Homework Statement



"Estimate the mass of water in all the World’s oceans."


Homework Equations



I know the following:
Two-thirds of the Earth is sea.
The density of seawater is 1025 kg/m3.
Radius of the Earth = 6.3*106m.


The Attempt at a Solution



Let's assume that the Earth's crust is a spherical shell that has a thickness of 0.001 times the radius of the earth.
So, the volume of the crust = (4[tex]\pi[/tex]r2)(router-rinner) = 3.1*1018 m3.
So, volume of seawater = 2.1*1018 m3.
So, mass of seawater = 2.1*1021 kg.

Is the answer reasonable? How might I improve it?
 
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  • #2
no no, ~2/3 of the SURFACE of the Earth is ocean. much much less of the entire Earth is ocean. I'd recommend using the average depth of the ocean, and the surface area of the earth.
 
  • #3
"no no, ~2/3 of the SURFACE of the Earth is ocean. much much less of the entire Earth is ocean.": I am reading the 'surface' as the crust (or the outer layer) of the earth. I think that's what I have used in the calculation, not ~2/3 of the entire volume of the earth.

" I'd recommend using the average depth of the ocean, and the surface area of the earth. ":
I think that's what I did above.

I'd be glad if you could offer some genuine help.
 
  • #4
hasan_researc said:
I'd be glad if you could offer some genuine help.
Very sorry! I took, "Two-thirds of the Earth is sea" to mean that you thought that 'two-thirds of the Earth was sea.' I clearly should have known you meant something completely different.

Your numbers look good; your radius is a little big, but your density a little small (for sea-water), you should be within a factor of two.
 
  • #5


I would suggest that the answer provided is a reasonable estimation based on the given information. However, there are several ways we can improve the accuracy of this estimation.

1. Consider the actual shape of the Earth: While assuming the Earth's crust to be a spherical shell is a good approximation, it is not entirely accurate. The Earth's shape is more accurately described as an oblate spheroid, which means it is flattened at the poles and bulging at the equator. This can affect the volume and mass calculations.

2. Consider the depth of the oceans: The given information only mentions the two-thirds of the Earth's surface is covered by oceans, but it does not specify the average depth of the oceans. Accounting for the varying depths of the oceans can significantly impact the estimation of the mass of water.

3. Use more precise measurements: The given radius of the Earth is rounded to one significant figure. Using a more precise measurement, such as 6,371 km, can improve the accuracy of the estimation.

4. Account for salt content and temperature: The density of seawater varies based on the salt content and temperature. The given density of 1025 kg/m3 is an average value. Taking into account the variations in density can result in a more accurate estimation.

5. Use more data points: The given information only mentions the two-thirds of the Earth's surface and the density of seawater. Including more data points, such as the average depth of the oceans and the actual shape of the Earth, can lead to a more accurate estimation.

Overall, while the provided estimation is reasonable, incorporating more precise measurements and data points can result in a more accurate answer. As a scientist, it is important to continuously improve and refine our estimations and calculations to increase the accuracy of our results.
 

FAQ: How Accurate Is Our Estimation of the World’s Ocean Mass?

What is a numerical estimation problem?

A numerical estimation problem is a mathematical problem that requires a person to make an educated guess or approximation of the answer, rather than solving it exactly. It typically involves using basic mathematical operations such as addition, subtraction, multiplication, and division to arrive at a close estimate of the answer.

Why is numerical estimation important?

Numerical estimation is important because it helps us quickly and efficiently solve problems in our daily lives that require approximate solutions. It also allows us to check the reasonableness of our answers and make sure we haven't made a mistake in our calculations.

What strategies can be used to solve a numerical estimation problem?

There are several strategies that can be used to solve a numerical estimation problem, including rounding, front-end estimation, clustering, and compatible numbers. These strategies involve simplifying the numbers in the problem to make the estimation process easier and more accurate.

How can numerical estimation be used in real-life situations?

Numerical estimation is used in a variety of real-life situations, such as budgeting, grocery shopping, cooking, and measuring. It allows us to quickly estimate costs, quantities, and measurements without having to perform complex calculations.

What are some common mistakes to avoid when solving a numerical estimation problem?

Some common mistakes to avoid when solving a numerical estimation problem include not using the appropriate estimation strategy, not taking into account significant figures, and not double-checking the reasonableness of the estimated answer. It is also important to make sure all numbers are correctly rounded and that units are included in the final answer, if applicable.

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