Easy Circular Motion Problem that I can't get right

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SUMMARY

The discussion centers on calculating the speed of a satellite in circular motion, specifically the Westar VI satellite orbiting 470 km above Earth. The centripetal acceleration is given as 8.19 m/s², and the radius of the Earth is 6370 km. The user correctly applies the formula a = v²/r but miscalculates the conversion from m/s² to km/h², leading to an incorrect final speed of 2694.46 km/h instead of the expected value. The error lies in the conversion process, which needs to be accurately executed to avoid discrepancies.

PREREQUISITES
  • Circular motion physics principles
  • Understanding of centripetal acceleration
  • Conversion between units of measurement (m/s to km/h)
  • Basic algebra for solving equations
NEXT STEPS
  • Review the derivation of the centripetal acceleration formula a = v²/r
  • Practice unit conversions, specifically from m/s to km/h
  • Explore examples of circular motion problems involving satellites
  • Investigate the effects of altitude on satellite speed and acceleration
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Students studying physics, educators teaching circular motion concepts, and anyone interested in satellite dynamics and orbital mechanics.

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The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 470. km above the Earth's surface, where the free-fall acceleration (centripetal acceleration) is 8.19 m/s2. Take the radius of the Earth as 6370 km.

Determine the speed of the satellite in km/h.


THis is a circular motion problem where a = v^2/r can be used right?
8.19 m/s^2 converted to km/h^2 = 1061.42 km/h^2

sqrt(1061.424*(470+6370) = 2694.46

my answer was 2694.46; 2690 but the system is telling me that I'm off by a multiple of ten. What am I doing wrong?
 
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I think your conversion from m/s to km/h is wrong...
 

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