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    Gravitational acceleration and pendulum period on planets

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    My question which I am not exactly sure is :
    1.I need to find the mass and radius of three of the nine planets in our solar system. I need to be sure that the masses are expressed in kilograms and the radii are expressed in meters.
    2.Using data, I need to find out how to calculate the gravitational acceleration on each of the three planets selected. Note: With the masses measured in kilograms and the radii in meters, the units of gravitational acceleration would turn out to be meters per squared seconds.
    3.Use the gravitational accelerations that was calculated in Step 2 to find the period of a 2 meter long simple pendulum on each of the three planets. Note: The length of a simple pendulum is normally expressed in meters, so it is sufficient to replace L with the number 2 in the period expression.

    I do know when solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i).

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    Solution Preview

    Please see detailed solution in the attached file.

    g_earth = 9.8 m/s^2
    g_mercury = 3.7 m/s^2
    g_saturn = 24.8 m/s^2

    In the real world, where might these imaginary numbers be used?

    It is ...

    Solution Summary

    The solution explains on how to calculate the period of the simple pendulum. It also elaborates how it is affected by the gravitational acceleration, which is dependent on the mass and radius of the planets. The solution includes step-by-step examples on three of nine planets of the solar system.