Centripetal Acceleration of space shuttle

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SUMMARY

The discussion focuses on calculating the centripetal acceleration and velocity of a space shuttle in low Earth orbit, specifically at a distance of 1.6 x 10^5 m above the Earth's surface. The radius used for calculations is 6.54 x 10^6 m, which combines the Earth's radius and the shuttle's altitude. The equation for centripetal acceleration, Ac = v² / r, is utilized to derive the shuttle's velocity, leading to a calculated speed of approximately 8006 m/s. However, the correct orbital speed is 7810 m/s, which aligns with a gravitational acceleration of 9.3 m/s², highlighting the importance of accurate gravitational values in orbital mechanics.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula (Ac = v² / r)
  • Knowledge of gravitational acceleration values (e.g., 9.8 m/s², 9.3 m/s²)
  • Familiarity with the concept of orbital mechanics and circular orbits
  • Basic algebra skills for manipulating equations and solving for variables
NEXT STEPS
  • Study the derivation of orbital velocity formulas in circular motion
  • Learn about gravitational constants and their application in orbital calculations
  • Explore the relationship between mass, gravity, and centripetal force in space environments
  • Investigate the effects of altitude on gravitational acceleration and orbital speed
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and orbital dynamics, as well as educators looking for practical examples of centripetal acceleration in real-world applications.

E.M.S
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Homework Statement



"The Space shuttle is located in a low orbit at a distance of 1.6 x 10^5 m above the surface of the earth. If gravity is the only force acting on the shuttle, what is the shuttle's speed while in this orbit?"

Variables:
Shuttle Velocity = ?
r = 1.6e5 + 6.38e6 (radius of the earth) = 6.54e6

Homework Equations



Ac = v2 / r

The Attempt at a Solution



I'm having issues because of the lack of information. The only givens in the problem are the distance of the shuttle and the radius of the earth. My idea was that if Ac = v2 / r, then the velocity would be the sqroot of Ac x r. Since the mass of the shuttle is not given, i can't calculate the actual value of gravity, so I assume they want me to use 9.8 m/s2. Multiplying 9.8 x 6.54e6 (The value of the Earth radius plus shuttle distance) = 6.41e7, the sq root of this is 8006 m/s. The actual answer to the problem is 7810 - which makes sense in the context of a gravity value of 9.3 m/s2, but because this information was not given in the problem and the mass of the shuttle was not given so that the actual gravity could be derived, I am still at a loss for how I'm supposed to come up with this answer.
 
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Okay nevermind on this, I just realized that I was also given the equation for the radius of a circular orbit (r = G (mass Earth / v 2)), and everything fits when I plug it into that equation.
 
i think the equation for circular orbit would be
radius=gravity(mass of earth/velocity^2)
Try plugging in your knowns
 

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