An object is launched from the surface of the Earth with speed v1 at an angle θ = 30◦ to an axis perpendicular to the surface. The object’s low-orbit path is displayed in the figure below, reaching a maximum height (called apogee) of 3R⊕ from the Earth’s center, where R⊕ = 6371 km. The mass of the Earth is M⊕ = 5.972 × 1024 kg. a. Is angular momentum conserved relative to the center of the Earth?   b. Is energy conserved in this motion?  c. What is the projectile’s launch speed from the surface, v1, and its speed at apogee, v2?

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.