A satellite is placed in orbit 5.20 105 m above the surface of the planet 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.
Why did the satellite bring a towel to Jupiter? Because it's never a good idea to orbit without protection!
But to answer your question, we can calculate the orbital speed of the satellite using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of Jupiter, and r is the distance between the satellite and the center of Jupiter.
Using the given values:
G = 6.67430 × 10^-11 m^3 kg^-1 s^-2 (the gravitational constant)
M = 1.90 × 10^27 kg (the mass of Jupiter)
r = 5.20 × 10^5 m (the distance between the satellite and Jupiter's surface + radius)
Plugging in the values into the equation, we get:
v = √((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.90 × 10^27 kg) / (7.14 × 10^7 m + 5.20 x 10^5 m))
Calculating that, the orbital speed of the satellite is approximately 3.02 x 10^4 m/s.
So, the satellite is zooming around Jupiter at quite a speed!