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physics A-Level Physics
 
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Relationship between Gravitational Force and Centripetal Acceleration

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Detailed solution steps are available at:
 
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Example 1.

Engineers want to test a new cannon that provides a long-range projection.

  • What speed does a projectile need to orbit the Earth just above the ground when it is projected from the ground?

  • How much speed is needed for this projectile to completely leave the Earth's attraction?

  • What would be the mass of the Earth so that even a projectile that could reach the speed of light would not escape its gravity? The mass of the Earth is , its radius is 6400 km, and the speed of light is . Assume that the atmosphere has no effect on the projectile.

    
Example 2.

At what altitude above the Earth's surface is the gravitational acceleration half the magnitude on its surface? The radius of the Earth is 6370 km.

    
3.

Two satellites orbit the Earth. The orbit radius of the second satellite is twice that of the orbit radius of the first satellite. What is the ratio of the speed of the first satellite to that of the second satellite?

    
4.

Two stars of equal mass orbit a common centre as shown in the figure. The period of both stars is 80 years. What is the distance between the stars? The gravitational constant is .


    
5.

Two satellites, each weighing 1 tonne, orbit the Earth on the same orbit. The distance between them is 100 m. At what acceleration are the satellites moving towards each other? The gravitational constant is .