The radius of Saturn (from the center to just above the atmosphere) is 60300 km (60300✕103 m), and its mass is 570✕1024 kg. An object is launched straight up from just above the atmosphere of Saturn.
What initial speed is needed so that when the object is far from Saturn its final speed is 28000 m/s?
I'm using ΔE + ΔU = 0 and then I'm trying to derive the equation needed to solve it with the information I have. So I get Vi = sqrt(Vf^2 + 2GMs(1/Δr))
Ms = mass of saturn
The Attempt at a Solution
The answer is 45300 m/s, but I'm getting something way higher with the equation I'm using.