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CIRCULAR  MOTION

 

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Uniform Circular Motion

 

 

 

 

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. In all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well An object undergoing uniform circular motion is moving with constant speed; nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards.

Satellite Motion

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  Launch Speed equal to 8000 m/s Projectile orbits Earth - Circular Path

  Launch Speed greater than 8000 m/s  Projectile orbits Earth - Elliptical Path

An orbiting satellite is a projectile in the sense that the only force acting upon an orbiting satellite is the force of gravity. Most Earth satellites are orbiting at a distance high above the Earth such that forces of air resistance do not influence their motion Second, a satellite is acted upon by the force of gravity and this force does accelerate it towards the Earth. In the absence of gravity a satellite would move in a straight line path tangent to the Earth. In the absence of any forces whatsoever, an object in motion (such as a satellite) would continue in motion with the same speed and in the same direction (the law of inertia ). Earth curves approximately 5 meters downward for every 8000 meters along its horizon In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of 8000 meters before falling a vertical distance of 5 meters. Since a horizontally-launched projectile falls a vertical distance of 5 meters in its first second of motion, a orbiting projectile must be launched with a horizontal speed of 8000 m/s. When launched at this speed, the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite. A cannonball launched with speeds less than 8000 m/s would eventually fall to the Earth. A cannonball launched with a speed of 8000 m/s would orbit the Earth in a circular path. Finally, a cannonball launched with a speed greater than 8000 m/s would orbit the Earth in an elliptical path

  Planetary Motion 

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