Satellite motion

Definition

Satellite motion refers to the movement of a satellite around a celestial body, such as a planet or moon, due to the gravitational force exerted by that body. This motion is governed by the principles of Newtonian mechanics, specifically the gravitational potential and the laws of motion, which describe how satellites maintain their orbits and how factors like velocity and distance from the central body influence their paths.

5 Must Know Facts For Your Next Test

1. Satellites must achieve a specific orbital velocity to maintain their orbits; if they go too slow, they will fall back to the celestial body, and if they go too fast, they will escape into space.
2. The shape of a satellite's orbit can be circular or elliptical, depending on initial conditions and external forces acting upon it.
3. The gravitational potential energy of a satellite decreases as it moves closer to the central body, while its kinetic energy increases due to acceleration.
4. For a satellite in a stable orbit, the centripetal force needed to keep it in orbit is provided by the gravitational attraction of the central body.
5. Satellite motion can be influenced by factors such as atmospheric drag (for low Earth orbits), gravitational interactions with other bodies, and perturbations due to non-uniform mass distributions.

Review Questions

• How does gravitational force impact satellite motion and what are the key factors that determine the stability of an orbit?
  • Gravitational force is crucial in satellite motion as it provides the necessary centripetal force that keeps satellites in orbit around celestial bodies. The stability of an orbit depends on factors like orbital velocity, distance from the central body, and the mass of that body. If these factors are balanced correctly, a satellite can maintain a stable orbit; otherwise, it may spiral inwards or escape into space.
• Explain how orbital velocity is derived from Newton's law of gravitation and its role in determining satellite motion.
  • Orbital velocity can be derived from Newton's law of gravitation, which states that the gravitational force between two masses is proportional to their masses and inversely proportional to the square of their separation distance. By setting this gravitational force equal to the centripetal force required for circular motion, we find that orbital velocity is given by the formula $$v = \\sqrt{\frac{GM}{r}}$$, where $$G$$ is the gravitational constant, $$M$$ is the mass of the central body, and $$r$$ is the radius of orbit. This relationship shows how a satellite's speed determines its ability to remain in orbit.
• Analyze how non-uniform mass distributions can affect satellite motion and lead to orbital perturbations over time.
  • Non-uniform mass distributions within a celestial body can lead to variations in gravitational pull experienced by satellites, causing orbital perturbations. These perturbations can result from uneven density in planets or moons that create regions of higher or lower gravity. Over time, these effects can cause satellites to experience changes in their orbital paths, potentially leading to drifting from their original trajectories or changes in orbital stability. Understanding these variations is essential for accurate long-term predictions of satellite behavior.

Related terms

gravitational force: The attractive force between two masses, which is responsible for the orbits of satellites and other celestial bodies.

orbital velocity: The speed required for an object to maintain a stable orbit around a celestial body, dependent on the mass of the body and the distance from its center.

Kepler's laws: A set of three fundamental laws that describe the motion of planets and satellites in elliptical orbits, formulated by Johannes Kepler in the early 17th century.