GCSE Physics Tutorial: Stable Orbits and Radius-Speed Relationship

In this tutorial, we will explore how the radius of an orbit must change if the speed of an object in a stable orbit changes.

Stable Orbits and the Radius-Speed Relationship

The stability of an orbit depends on a delicate balance between the gravitational force and the centrifugal force. When an object is in a stable orbit, such as a satellite around a planet, any change in its speed will necessitate a corresponding change in its orbital radius.

Centrifugal Force and Gravity

1. Centrifugal Force: The centrifugal force is the apparent outward force experienced by an object moving in a curved path. It arises due to the object's inertia, which resists being pulled towards the center of the orbit.

2. Gravitational Force: The gravitational force pulls the object towards the center of the massive body it is orbiting.

Changing Speed and Radius

When the speed of an object in a stable orbit changes, the balance between the centrifugal force and the gravitational force is disrupted. To maintain a stable orbit, the radius of the orbit must adjust to accommodate the new speed.

• Increased Speed: If the object's speed increases, the centrifugal force will become stronger. To counteract this increased outward force, the gravitational force needs to become stronger as well. This can only be achieved by moving the object closer to the center of the orbit, reducing the radius.

• Decreased Speed: If the object's speed decreases, the centrifugal force will weaken. To restore the balance, the gravitational force must also weaken. This is accomplished by moving the object farther away from the center of the orbit, increasing the radius.

Conservation of Angular Momentum

In addition to the gravitational and centrifugal forces, the conservation of angular momentum also plays a role. Angular momentum is the product of an object's moment of inertia and its angular velocity. In a stable orbit, the angular momentum is conserved. When an object changes its speed, its angular velocity changes, and to maintain angular momentum, the radius must also change.

Conclusion

For an orbit to remain stable, any change in the speed of an object must result in a corresponding change in its orbital radius. The balance between the gravitational force and the centrifugal force, along with the conservation of angular momentum, ensures that the object maintains a stable path around the massive body it is orbiting. This delicate interplay between forces and motion is essential for the harmony of celestial orbits.

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