A satellite is placed in orbit 7.70 105 m above the surface of Jupiter. Jupiter has a mass of 1.90 1027 kg and a radius of 7.14 107 m. Find the orbital speed of the satellite.
I suggest you review Kepler's third law. You will find the equation you need there.
Another way to do it is to set
V^2/R = G M/R^2 where G is the universal constant of gravity, and M is the mass of Jupiter, and solve for V.
Make sure you use the distance of the satellite from the CENTER of Jupiter in the formula. It is
R = 7.217*10^7 m
To find the orbital speed of the satellite, we can use the formula for the orbital speed of a satellite around a planet:
V = √(G * M / r)
Where:
V is the orbital speed of the satellite,
G is the gravitational constant (6.67430 × 10^-11 N m^2 / kg^2),
M is the mass of the planet (Jupiter),
r is the distance between the center of the planet and the satellite.
Now let's plug in the values:
M = 1.90 × 10^27 kg (mass of Jupiter)
r = 7.14 × 10^7 m (radius of Jupiter + the distance of the satellite from the surface)
G = 6.67430 × 10^-11 N m^2 / kg^2 (gravitational constant)
V = √(6.67430 × 10^-11 N m^2 / kg^2 * 1.90 × 10^27 kg / (7.14 × 10^7 m))
Now let's calculate the value using the given values:
V = √(12.600147 × 10^16 N * m^2 / (7.14 × 10^7 m))
V = √1.762085 × 10^10 m^2 / s^2
Now let's simplify it:
V = 4.196417 × 10^5 m / s
Therefore, the orbital speed of the satellite is approximately 4.20 × 10^5 m/s.