Answer :
Jupiter can never be farther from the sun than Saturn if the mass of the sun is 1991030 kg, the orbital radius of Jupiter is 7781011 m, and the orbital radius of Saturn is 1431012 m.
Fc = m v² / r
Fg = G M m / r²
Fc = Centripetal force
Fg = Gravitational force
m = Mass of planet
v = Linear Velocity of planet
r = Orbit radius
G = Gravitational constant
M = Mass of sun
Fc = Fg
G M m / r² = m v² / r
v² = G M / r
M = 1991030 kg
G = 6.67 * [tex]10^{-11}[/tex] N m² / kg²
v² = G M / r
For Jupiter,
r = 7781011 m
vj² = 6.67 * [tex]10^{-11}[/tex] * 1991030 / 7781011
vj² = 1.17 * [tex]10^{-11}[/tex]
vj = 3.42 * [tex]10^{-6}[/tex] m / s
For Saturn,
r = 1431012 m
vs² = 6.67 * [tex]10^{-11}[/tex] * 1991030 / 1431012
vs² = 9.28 * [tex]10^{-11}[/tex]
vs = 9.63 * [tex]10^{-6}[/tex] m / s
vs > vj
Therefore, Jupiter can never be farther from the sun than Saturn
The given question is incomplete. The complete question is :
Suppose the sun's gravity were switched off. the planets would leave their orbits and fly away in straight lines as described by newton's first law. (assume the mass of the sun is 1991030 kg, the orbital radius of Jupiter is 7781011 m, and the orbital radius of Saturn is 1431012 m. Would Jupiter ever be farther from the Sun than Saturn?
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