Period of the Earth a long time ago

In summary, the period of the Earth 540 million years ago is 1.11 days, which may be affected by various factors and could be further refined through comparison with other sources and using different calculation methods.
  • #1
Ai52487963
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Homework Statement


Find the period of the Earth 540,000,000 years ago.

Homework Equations


[tex]

\frac{dL}{dt} = -2/5 MR^2 \frac{2 \pi}{P^2} \frac{dP}{dT} = -2/5 MR^2 \frac{2 \pi}{P^2_{t}} \left(\frac{dP}{dT}\right)_t

\par \left(\frac{dP}{dT}\right)_t = .0016 sec / century
\par P_t = 24 hours

[/tex]

The Attempt at a Solution



[tex]
\frac{dP}{P^2} = \left(\frac{dP}{dT}\right)_t \frac{1}{P^2} dt

\par \left(\frac{dP}{dT}\right)_t \frac{1}{P^2_t} \Rightarrow \alpha

\par \int^{then}_{now}\frac{dP}{P^2} = \alpha \int^{then}_{now} dt

\par \Rightarrow -\frac{1}{P_{then}} + \frac{1}{P_{now}} = \alpha t_then

\par P_{then} = \frac{1}{\frac{1}{P_{now}} - \alpha t_{then}}[/tex]

The period I get for the Earth 540 million years ago, for some reason, is 1.11 days. It should be .90 (or, the inverse of my answer). Is my math ok? My units all check out, but my period is longer, not shorter.
 
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  • #2


Your math appears to be correct, but there may be some factors that could affect the accuracy of your answer. For example, the Earth's rotation is affected by factors such as the distribution of landmasses and changes in the Earth's shape, which can vary over long periods of time. Additionally, there may be errors in the data used to calculate the Earth's rotational period 540 million years ago. It is also possible that there are other factors that you have not taken into account in your calculation.

To ensure the accuracy of your answer, it would be helpful to compare your result with other sources and see if they are consistent. You could also try using different equations or methods to calculate the Earth's rotational period and see if you get a more accurate result. Overall, while your math appears to be correct, there may be other factors that could affect the accuracy of your answer.
 

What is the period of the Earth a long time ago?

The period of the Earth a long time ago is known as the Precambrian era, which lasted from about 4.6 billion years ago to 541 million years ago.

What was the climate like during the Precambrian era?

The climate during the Precambrian era was extremely hot and humid, with no polar ice caps and high levels of carbon dioxide in the atmosphere.

What types of life existed on Earth during the Precambrian era?

During the Precambrian era, only single-celled organisms, such as bacteria and algae, existed on Earth. More complex forms of life did not appear until the beginning of the Cambrian period.

How did the Earth change during the Precambrian era?

During the Precambrian era, the Earth underwent significant changes, including the formation of the continents, the emergence of oxygen in the atmosphere, and the development of the first life forms.

What evidence do we have about the Precambrian era?

Scientists use various types of evidence, such as rocks, fossils, and chemical analysis, to study the Precambrian era. They also rely on the geological record and theories of plate tectonics to understand the Earth's early history.

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