A satellite is placed in orbit 2.75 x 105 m above the surface of Jupiter. Jupiter has a mass of 1.90 x 1027 kg and a radius of 7.14 x 107 m. Find the orbital speed of the satellite.

Jupiter's gravitational constant is

GM = 6.67259X10^(-11)(1.9X10^27)

The orbital radius R is 7.14x10^7 + 2.75x10^5

The velocity required for a satellite to remain in circular orbit derives from
V = sqrt[R/GM]

To find the orbital speed of the satellite, we can use the concept of gravitational force and the relationship between force, mass, radius, and speed.

The gravitational force between the satellite and Jupiter is given by the equation:

F = (G * m1 * m2) / r^2

Where F is the gravitational force, G is the universal gravitational constant (approximately 6.67 x 10^-11 N m^2 / kg^2), m1 is the mass of the satellite, m2 is the mass of Jupiter, and r is the distance between the satellite and the center of Jupiter.

At the orbital speed, the gravitational force acting on the satellite provides the necessary centripetal force to keep it in orbit. Therefore, we can equate the gravitational force with the centripetal force:

F = (m * v^2) / r

Where v is the orbital speed of the satellite and m is the mass of the satellite.

Now, let's solve for the orbital speed v:

(G * m1 * m2) / r^2 = (m * v^2) / r

Since m1 is negligible compared to m2 (mass of Jupiter), we can assume m1 << m2.

(G * m2) / r = v^2

Taking the square root of both sides:

v = √((G * m2) / r)

Now, let's substitute the given values:

m2 = 1.90 x 10^27 kg
r = 7.14 x 10^7 m
G = 6.67 x 10^-11 N m^2 / kg^2

v = √((6.67 x 10^-11 N m^2 / kg^2 * 1.90 x 10^27 kg) / (7.14 x 10^7 m))

Calculating the equation above will give us the value of the orbital speed in m/s.