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13 March, 03:59

In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler's third law?

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  1. 13 March, 04:06
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    772.65 years.

    Explanation:

    Semi major axis = R = 84 AU = 1.257 * 10¹³ m

    According to the 3rd law of Kepler, T² = 4 π² R³ / GM

    Here R is the semi major axis. G = 6.67 * 10⁻¹¹ SI units.

    M is the mass of the Sun = 1.98 x 10³⁰ kg

    T² = 4 (3.14) ³ (1.257 * 10¹³) ³: (6.67 * 10⁻¹¹) (1.98 x 10³⁰)

    ⇒ Time period = T = 2.44 x 10¹⁰ seconds

    1 s = 3.17 * 10⁻⁸ years

    Converting the seconds to years, T = 772.65 years.
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