Final answer:
The orbital speed of the satellite can be found using the equations for gravitational force and centripetal acceleration. By equating these two equations, we can solve for the orbital speed. Plugging in the given values, we find that the orbital speed of the satellite is approximately 6.43 x 10^3 m/s.
Step-by-step explanation:
To find the orbital speed of the satellite, we can use the equation for gravitational force: F = ma, where F is the gravitational force, m is the mass of the satellite, and a is the centripetal acceleration. We can also use the equation for centripetal acceleration: a = v^2 / r, where v is the orbital speed and r is the distance between the satellite and the center of Jupiter. By equating the two equations, we can solve for v.
The gravitational force acting on the satellite is given by the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 is the mass of Jupiter, and r is the distance between the satellite and the center of Jupiter.
Plugging in the values given in the question, we can solve for v:
v^2 = (G * m1) / r
v = sqrt((G * m1) / r)
Using the given values of m1 = 1.90 x 10^27 kg, r = 8.52 x 10^5 m, and the gravitational constant G = 6.67 x 10^-11 Nm^2/kg^2, we can calculate the orbital speed of the satellite:
v = sqrt((6.67 x 10^-11 Nm^2/kg^2 * 1.90 x 10^27 kg) / (8.52 x 10^5 m))
v ≈ 6.43 x 10^3 m/s