What Units Should I Use to Calculate Planetary Orbit Time?

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SUMMARY

The discussion focuses on calculating the time it takes for a planet to form from a protoplanetary disk using the equation t = (3/A)M^(1/3), where A is defined as ((1+2β)σ/P)((3π²/4ρ_m)^(2/3)). The user is uncertain about the appropriate units for time, debating between days and seconds. The consensus leans towards using seconds for precision in calculations, as days may lead to ambiguity in the results. Additionally, a query regarding LaTeX formatting for large brackets around fractions was addressed with the solution of using "\left(" and "\right)".

PREREQUISITES
  • Understanding of planetary formation and protoplanetary disks
  • Familiarity with the equation t = (3/A)M^(1/3)
  • Knowledge of LaTeX for mathematical formatting
  • Basic grasp of unit conversion in scientific calculations
NEXT STEPS
  • Research the implications of using different time units in astrophysical calculations
  • Explore advanced LaTeX techniques for mathematical expressions
  • Study the dynamics of protoplanetary disks in planetary formation
  • Learn about the significance of the parameters β, σ, P, and ρ_m in the context of the equation
USEFUL FOR

Astronomers, astrophysicists, students studying planetary science, and anyone involved in mathematical modeling of planetary formation processes.

lagwagon555
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Hi all, I'm working on a problem where I have to find the time it takes for a planet to form from a protoplanetary disk, using the equation:

[tex]t = \frac {3}{A}M^{1/3}[/tex]

Where

[tex]A= ( \frac {(1+2\beta)\sigma}{P}) (\frac {3\pi^2}{4\rho_m})^{2/3}[/tex]

However, I'm not sure which units the periods should be calculated with. Results from google seem to use both, and the units I'm given for in the question are days. However, seconds would seem the logical thing to use. Calculating using both, and choosing the best answer won't really work, since I have no idea how long a sensible answer would be. Any suggestions? Thanks.

Incidentally, does anyone know how to get large brackets around fractions, when using Latex?
 
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The protoplanetary disk when a star system is very unstable and is the building blocks of a planetary system. Here is an interesting site you may find interesting:

http://www.iop.org/EJ/article/0004-637X/581/1/681/55760.web.pdf?request-id=18af475d-f2da-407a-ba2f-0a3e870da81b
 
LaTeX

Hi lagwagon555! :smile:
lagwagon555 said:
Incidentally, does anyone know how to get large brackets around fractions, when using Latex?

Type "\left(" and "\right)" :wink:

(also works with {} [] ||)
 
Last edited:

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