How can a satellite's speed decrease without its angular momentum changing?

Angular momentum (L) is a measure of the rotational motion of an object and is given by the product of its mass (m), its speed (v), and its distance (r) from the center of rotation (the center of the planet, in this case). Mathematically, it can be expressed as: L = m * v * r The conservation of angular momentum states that, in the absence of external torques, the angular momentum of an object remains constant.

Based on the equation for angular momentum, L = m * v * r, we can see that there are three factors affecting angular momentum: mass (m), speed (v), and distance from the center of rotation (r).

As the conservation of angular momentum states that the angular momentum of an object remains constant if no external torques act upon it, we can deduce that if one of the factors changes, the other factor(s) must change in a way that keeps the product m * v * r constant.

If we want the satellite's speed (v) to decrease without changing its angular momentum (L), then the other factors in the equation L = m * v * r, that is mass (m) and distance (r), must change accordingly. Since the mass of a satellite cannot be changed while it is in orbit, the only variable left that can be altered is the distance (r) between the satellite and the center of the planet. If the satellite's speed decreases, the distance (r) must increase in order to keep the product m * v * r, and therefore the angular momentum (L), constant. In conclusion, a satellite's speed can decrease without changing its angular momentum by increasing its distance from the center of the planet it's orbiting. This can happen, for instance, when the satellite moves to a higher orbit due to some external factors such as the gravitational interaction with other celestial bodies.