Question

Consider the four Galilean moons of Jupiter: Io, Europa, Ganymede, and Callisto. Use the data below to find the average magnitude of the gravitational force that the Jupiter exerts on each of those moons. Use scientific notation and round the coefficient to two decimals. See info for this homework if you're not sure about the format.
Jupiter's mass: 1.9×10²⁷ kg

Moon:	Mass (kg)	Average orbital distance from Jupiter (m)
Io	8.93×10 22	4.22×10 8
Europa	4.80×10 22	6.71×10 8
Ganymede	1.48×10 23	1.07×10 9
Callisto	1.08×10 23	1.88×10 9

F_Io = ____N
F_Europa = ____ N
F_Ganymede = ____ N
F_Callisto = ____ N

Answer 1

Gravitational Force is given by:

F = G*m1*m2/R^2

m1, m2 = mass of planets/objects

R = distance between both masses

G = Gravitational constant = 6.67*10^-11

Part A.

Force between Jupiter and Io

F = G*m1*m2/R^2

m1 = mass of Jupiter = 1.9*10^27 kg

So,

F = 6.67*10^-11*1.9*10^27*8.93*10^22/(4.22*10^8)^2

F = 6.35*10^22 N

Part B

Force between Jupiter and Europa

F = G*m1*m2/R^2

m1 = mass of Jupiter = 1.9*10^27 kg

So,

F = 6.67*10^-11*1.9*10^27*4.80*10^22/(6.71*10^8)^2

F = 1.35*10^22 N

Part C.

Force between Jupiter and Ganymede

F = G*m1*m2/R^2

m1 = mass of Jupiter = 1.9*10^27 kg

So,

F = 6.67*10^-11*1.9*10^27*1.48*10^23/(1.07*10^9)^2

F = 1.64*10^22 N

Part D.

Force between Jupiter and Callisto

F = G*m1*m2/R^2

m1 = mass of Jupiter = 1.9*10^27 kg

So,

F = 6.67*10^-11*1.9*10^27*1.08*10^23/(1.88*10^9)^2

F = 3.87*10^21 N

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