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Mars' orbit has a diameter 1.52 times that of the earth's orbit. how long does it take mars to orbit the sun?

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mars' orbit has a diameter 1.52 times that of the earth's orbit. how long does it take mars to orbit the sun?(period of the earth =365 days)

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  1. 668 days from memory


  2. Average orbital speed of Mars = 24.077 km/s

    Average orbital speed of Earth = 29.783 km/s

    Earth's orbit = Earth's velocity x Time taken for Earth to orbit the sun =365 x 24 x 60 x 60 x 29.783 =939236688 km

    Time taken for Mars to orbit the sun = Mars's orbit / Mars's average orbital speed = 1,52 x Earth's orbit / Mars's average orbital speed = 59294752 s = 686,282 Earth days

  3. We know that an object in orbit around another has centrifugal force F = (mv^2)/r

    We know that the force on an object due to gravity is F=GMm/r^2 where G is the universal gravitational constant, M is the mass of the sun and m is the mass of the orbiting object (in this case Mars).

    Equating these two gives us

    GMm/r^2   =   (mv^2)/r

    Rearanging for v

    v= Squareroot(GM/r)

    Now, velocity = distance / time.

    So for an object moving in a circle of diameter D and taking time t to do it,

    v=pi*D/t.        note D=2r, so v=2pi*r/t.

    Rearange for t:  

    t = 2*pi*r/v.

    Sub in v from our original equation and we have

    t= 2pi*r*Squareroot(r/GM).

    If Mars' orbit is 1.52* Earth orbit, then plug in the numbers

    (G = 6.67*10^(-11)             Earth Orbit = 1.5*10^11

    M = 2*10^30                     Mars Orbit r = 1.52*Earth Orbit

    This comes out as about 685days.



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