Angular momentum of a satellite (a) What is the angular...

Angular momentum of a satellite (a) What is the angular momentum (referred to the center of the orbit) of a satellite of mass $M_{\mathrm{s}}$ that moves in a circular orbit of radius $r ?$ The result is to be expressed in terms only of $r, G, M_{e}, M_{e}$ (the mass of the earth). (b) For $M_{n}=100 \mathrm{~kg}$, what is the numerical value (in egs units of the angular momentum of an orbit for which the radius is twice the radius of the earth?

Angular momentum of a satellite
(a) What is the angular momentum (referred to the center of the orbit) of a satellite of mass $M_{\mathrm{s}}$ that moves in a circular orbit of radius $r ?$ The result is to be expressed in terms only of $r, G, M_{e}, M_{e}$ (the mass of the earth).
(b) For $M_{n}=100 \mathrm{~kg}$, what is the numerical value (in egs units of the angular momentum of an orbit for which the radius is twice the radius of the earth?

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Key Concepts

Angular Momentum in Orbital Mechanics

In orbital mechanics, angular momentum is the measure of the rotational motion of a body about a central point. For a satellite in a circular orbit, the angular momentum is defined as the product of its mass, orbital radius, and tangential velocity (L = m·r·v). This quantity is conserved in a closed system under central forces, making it a crucial concept for understanding satellite trajectories and stability.

Orbital Velocity in a Circular Orbit

The orbital velocity of a satellite in a circular orbit is determined by setting the gravitational force equal to the required centripetal force for circular motion. This leads to the expression v = ?(G·M?/r), where G is the gravitational constant and M? is the mass of the primary body, such as Earth. Substituting this expression for v into the angular momentum formula gives L = M?·?(G·M?·r), which is fundamental to solving problems related to satellite motion.

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