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.

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

The answer to the question is c.