Need help with escape velocity practice problem

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SUMMARY

The discussion centers on calculating the initial speed required for an object to reach a final speed of 28000 m/s when launched from Saturn's atmosphere. The relevant parameters include Saturn's radius of 60300 km and its mass of 570×1024 kg. The correct formula derived from energy conservation principles is Vi = sqrt(Vf2 + 2GMs(1/Δr)). The final calculated initial speed is 45300 m/s, achieved after correcting unit conversion errors in the initial attempts.

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  • Understanding of gravitational potential energy and kinetic energy concepts
  • Familiarity with the equation for escape velocity
  • Knowledge of unit conversion in physics
  • Basic algebra and square root calculations
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  • Learn about gravitational potential energy and its applications in astrophysics
  • Explore advanced unit conversion techniques in physics problems
  • Practice solving problems involving energy conservation in celestial mechanics
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Homework Statement



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?


Homework Equations



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.
 
Physics news on Phys.org
Just kidding. Figured it out, I messed up on the unit conversions.
 

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