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30 January, 20:58

Io, a satellite of jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 105 km. from these data, determine the mass of jupiter.

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  1. 30 January, 21:09
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    First step is to convert the units into standard units (km into m and days into sec)

    1.77 days = 1.77 * 24 * 60 * 60 = 152928 seconds

    4.22 * 10^5 = 4.22 * 10^5 * 10^3 = 4.22 * 10^8 meters

    Second step is to start solving,

    We will use these two rules:

    rule #1: velocity = distance/time (distance is the circumference=2*pi*radius)

    rule #2: velocity = (GM/r) ^0.5 (G is a constant = 6.7 * 10^-11)

    equating the two rules, we find that:

    M = (2*pi*r / T) ² (r / G)

    Substituting in the previous equation, we will find that:

    M = 1.8999 * 10^27 Kg
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