Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

Physics question?

a)Calculate the orbital radius of Pluto in AU if its orbital period is 248 Earth years.

b) Pluto’s largest moon, Charon (which is nearly half the size of Pluto!), has an

orbital period of 153 hours. Can you use the information from part a) to calculate

Charon’s orbital radius? Explain.??

c) One of Pluto’s smaller moons, Nix, has an orbital period of 24.85 days and an

orbital radius of 48 690 km. Calculate Charon’s orbital radius in km.

2 Answers

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  • 2 months ago

    a)Calculate the orbital radius of Pluto in AU if its orbital period is 248 Earth years.

    P = orbital period = 248 Earth years

    R = orbital radius = to be determined

    Kepler's Law of Periods (Third Law)

    R³ = P²

    R = ³√(P²)

    R = ³√(248²)

    R = 39.47308961 AU = 39.5 AU

    b) Pluto’s largest moon, Charon (which is nearly half the size of Pluto!), has an

    orbital period of 153 hours. Can you use the information from part a) to calculate

    Charon’s orbital radius? Explain.??

    No, the information from part (a) cannot be used because Kepler's Third Law in this

    form applies only to planets revolving around a star, not a moon revolving around a

    planet. The masses of both Pluto and Charon would be needed to do the calculation.

    c) One of Pluto’s smaller moons, Nix, has an orbital period of 24.85 days and an

    orbital radius of 48 690 km. Calculate Charon’s orbital radius in km.

    This question is confusing and nonsensical.

  • 2 months ago

    Kepler's law.  R^3/T^2 is a constant for all bodies around the SAME central body.  ie (R1/R2)^3 = (T2/T1)^2 so b) is not possible.

    a) Rp^3 = Re^3 * (Te/Tp)^2  -> Rp^3 = 248^2 Au -> Rp= 248^(2/3) = 39 AU

    c) Tc^2 = Tn^2 *(Rn/Rc)^3  Substitute to solve

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