Chap 8.10. Derivation of Kepler's Third law - quick redo.

00:02:28
https://www.youtube.com/watch?v=QcFjKumVkyw

Resumo

TLDRThe speaker revises Kepler's Third Law, known as the Law of Harmonies, which describes the motion of planets or satellites around a larger celestial body. The formula for the third law is presented in two different unit systems. Using astronomical units (AU), the relationship is T^2 ∝ A^3, where 'T' is the orbital period and 'A' is the semi-major axis. However, if using standard SI units such as meters and kilograms, the formula changes to T^2 = (4π²/GM) * r³. It is essential to use the correct formula based on the unit system to accurately describe planetary motion.

Conclusões

  • 🎓 Kepler's Third Law is called the Law of Harmonies.
  • 🪐 The law explains the motion of planets or satellites around larger celestial bodies.
  • 🔮 In astronomical units: T^2 ∝ A^3 (orbital period and semi-major axis relation).
  • 📏 For SI units, the formula requires masses and radii: T^2 = (4π²/GM) * r³.
  • 🔍 'GM' in the formula indicates the gravitational constant times the mass of the larger body.
  • ⚠️ Use appropriate formulas according to the unit system.
  • 💡 Important to differentiate between astronomical and SI units when applying formulas.

Linha do tempo

  • 00:00:00 - 00:02:28

    The speaker begins by reviewing Kepler's laws, specifically starting with Kepler's third law, known as the law of harmonics. This law describes planetary motion, stating that the square of the orbital period (T) is proportional to the cube of the semi-major axis of its orbit (a). The speaker explains the derivation of the formula using Newton's laws of motion and gravitation, highlighting the cancellation of terms and resulting in the relationship: T squared is proportional to r cubed. The speaker emphasizes using the correct units: astronomical units (AU) for the simplified form and SI units for the standard gravitational form, depending on the units of measure like meters or AU.

Mapa mental

Vídeo de perguntas e respostas

  • What is Kepler's Third Law?

    Kepler's Third Law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

  • What is the formula for Kepler's Third Law in astronomical units?

    In astronomical units, the formula is T^2 is proportional to A^3.

  • Can Kepler's Law be used with SI units?

    Yes, but you need to use the form: T^2 = (4π²/GM) r³ when using meters, kilograms, etc.

  • What is the Law of Harmonies?

    The Law of Harmonies is another name for Kepler's Third Law.

  • What is the significance of 'GM' in the equation?

    'GM' represents the gravitational constant multiplied by the mass of the larger object.

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Rolagem automática:
  • 00:00:00
    okay now going back to kepler's laws
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    [Music]
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    i'm gonna start backwards
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    so i'm gonna do kepler's third law first
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    we did this yesterday but i wanna just
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    revise
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    real quick
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    kepler's third law
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    what was kepler's third law
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    it was called the
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    law of harmonics
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    when a planet or anything moves around
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    another sun star or satellite moves
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    around the earth what can we write
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    sigma f equals
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    f
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    big g
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    four things moving in a circle means i
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    can write m v squared over r
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    equals g m m over r squared where r is
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    the radius
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    m is the mass of the tiny one and the m
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    is the mass of the big thing whatever
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    they may be so imagine it's the sun
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    so the little r
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    mass gets cancelled
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    i know v equals 2 pi r over t
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    for things moving in a circle
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    and plug that value in here what do i
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    get 4 pi squared r squared
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    divided by t
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    squared r equals
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    g m
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    over r squared
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    one of these r's gets cancelled
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    am i left with 4 pi squared over gm
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    r cubed equals t squared
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    or in astronomical units i can write t
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    squared is proportional to
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    a cube where a is a u
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    astronomical units
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    when can i use this one when i am using
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    a u's
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    or linear units or something like that i
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    cannot use this form for si units if i
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    am using s i units then i have to use
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    this form
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    got it please make sure to remember that
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    but you are unit
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    if your units are meters
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    kilograms and stuff then please use this
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    form if you're using a u then go ahead
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    and use this one
Etiquetas
  • Kepler's Third Law
  • Law of Harmonies
  • orbital period
  • gravitational motion
  • astronomical units
  • SI units
  • formula
  • planetary motion