with what orbital speed will a satellite circle Jupiter if placed at a height of 7.80 * 10 ^ 6 m above the surface of the planet? The mass of Jupiter is 1.90 * 10 ^ 27 kg and the radius of Jupiter is 7.14 * 10 ^ 7 * m .
To calculate the orbital speed of a satellite around Jupiter, we need to use the formula for orbital speed:
v = √(G * M / r)
Where:
v = Orbital speed
G = Gravitational constant (6.67 x 10^-11 m³/kg/s²)
M = Mass of Jupiter (1.90 x 10^27 kg)
r = Distance from the center of Jupiter to the satellite (radius of Jupiter + height above the surface)
First, let's solve for "r" by adding the radius of Jupiter to the height above the surface:
r = 7.14 x 10^7 m + 7.80 x 10^6 m
r = 8.92 x 10^7 m
Next, substitute the values into the orbital speed formula:
v = √(6.67 x 10^-11 m³/kg/s² * 1.90 x 10^27 kg / 8.92 x 10^7 m)
Calculating this equation will give us the value of the orbital speed 'v'.
v ≈ 1.31 x 10^4 m/s
Therefore, the satellite will circle Jupiter with an orbital speed of approximately 1.31 x 10^4 m/s.