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8 November, 20:11

Saturn has an orbital period of 29.46 years and it's average distance to the sun is 9.54 AU if Venus has an orbital period of 0.62 years what is its average distance to the sun in AU

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Answers (2)
  1. 8 November, 21:01
    0
    15.66 AU

    Explanation:

    Using Kepler's law which states that T² ∝ R³ where T = period of planet and R = distance of planet from sun.

    So T₁²/T₂² = R₁³/R₂³

    where T₁ = orbital period of Saturn = 29.46 years

    T₂ = orbital period of Venus = 0.62 years

    R₁ = average distance of Saturn to the sun = 9.54 AU

    R₂ = average distance of Venus to the sun = ?

    From the equation above,

    R₂³ = (T₂²/T₁²) R₁³

    R₂ = [∛ (T₂/T₁) ²]R₁

    R₂ = [∛ (0.62/29.46) ²]9.54 AU

    R₂ = [∛ (0.021) ²]9.54 AU

    R₂ = [∛0.000443]9.54 AU

    R₂ = [0.0762]9.54 AU

    R₂ = 0.727 AU
  2. 8 November, 21:32
    0
    Saturn orbital period

    p (s) = 29.46years

    Average distance

    a (s) = 9.54AU

    Venus orbital period

    p (v) = 0.62 years

    a (v) ?

    Using Kepler's third law

    a³ ∝p²

    a³ = kp²

    a³/p² = k

    Where

    a is the distance if planet from sun

    T is the period of the planet

    Then,

    a (Venus) ³/p (venus) ² = a (saturn) ³/p (saturn) ²

    a (v) ³/p (v) ² = a (s) ³/p (s) ²

    a (v) ³ / 0.62² = 9.54³/29.46²

    a (v) ³ / 0.62² = 1.0004

    a (v) ³ = 1.0004 * 0.62²

    a (v) ³ = 0.3846

    a (v) = cube root (0.3846)

    a (v) = 0.727 AU
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