Centripetal Acceleration of space shuttle

In summary, the conversation discusses the question of what the speed of the Space shuttle would be while in a low orbit above the Earth's surface, with the given information of the shuttle's distance from the surface and the radius of the Earth. The conversation includes attempts at solving the problem using the equation for centripetal acceleration and for circular orbit, but ultimately the solution is found by plugging in the known values into the equation for circular orbit.
  • #1
E.M.S
2
0

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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  • #2
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.
 
  • #3
i think the equation for circular orbit would be
radius=gravity(mass of earth/velocity^2)
Try plugging in your knowns
 

Related to Centripetal Acceleration of space shuttle

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that occurs when an object moves in a circular path. It is always directed towards the center of the circle and its magnitude is equal to v^2/r, where v is the velocity of the object and r is the radius of the circle.

2. How does centripetal acceleration affect the space shuttle?

The space shuttle experiences centripetal acceleration when it orbits around the Earth. This acceleration keeps the shuttle moving in a circular path around the Earth and prevents it from flying off into space.

3. How is the centripetal acceleration of the space shuttle calculated?

The centripetal acceleration of the space shuttle can be calculated using the formula a = v^2/r, where v is the orbital velocity of the shuttle and r is the radius of its orbit around the Earth. This can also be written as a = (2πr)/T^2, where T is the orbital period of the shuttle.

4. How does the centripetal acceleration of the space shuttle change during its orbit?

The centripetal acceleration of the space shuttle remains constant throughout its orbit. This is because the shuttle maintains a constant orbital velocity and distance from the Earth, resulting in a constant value for the acceleration.

5. What is the relationship between centripetal acceleration and centripetal force in the space shuttle?

The centripetal force required to keep the space shuttle in its circular orbit is equal to the centripetal acceleration multiplied by the mass of the shuttle. This force is provided by the gravitational pull of the Earth on the shuttle, which acts as the centripetal force in this scenario.

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