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Fields and Their Consequences

Orbits of planets and satellites

  • 7 things to know
  • Papers 2 and 3

Overview

Orbital speed and period, T² ∝ r³, the energy of an orbiting satellite, escape velocity and synchronous orbits.

What you need to know

Answer each one before you reveal it.

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Numbers

How are orbital speed and orbital period calculated for a satellite?

Numbers

Why does T² ∝ r³ hold, and what is the kinetic energy of an orbiting satellite?

Numbers

What is the potential energy of an orbiting satellite, and why is it negative?

Numbers

What is the total energy of an orbiting satellite, and what does a negative value mean?

Numbers

How do the kinetic and potential energies of a satellite compare, and what is escape velocity?

Numbers

How is escape velocity calculated, and what is a synchronous orbit?

Numbers

What is obtained by taking logarithms of T² = kr³, and what gradient results?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the formula for the orbital speed v of a satellite in a circular orbit of radius r around a central mass M.

    Model answer

    v = √(GM/r), where G is the gravitational constant and M is the central mass.

  2. 2

    In the orbital speed formula v = √(GM/r), what does each symbol represent?

    Model answer

    v is orbital speed, G is the gravitational constant, M is the mass of the central body, and r is the orbital radius.

  3. 3

    State the formula relating orbital period T to orbital radius r and orbital speed v for a circular orbit.

    Model answer

    T = 2πr/v

  4. 4

    Write the formula for orbital period T in terms of orbital radius r, gravitational constant G, and central mass M.

    Model answer

    T = 2π√(r³/GM)

  5. 5

    In deriving T² ∝ r³, what two forces are equated for a satellite in circular orbit?

    Model answer

    Gravitational force (GMm/r²) is equated to centripetal force (mv²/r).

  6. 6

    When gravitational force GMm/r² is equated to centripetal force mv²/r, what expression is obtained for v²?

    Model answer

    v² = GM/r

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