"In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies."
An equation used to calculate the velocity of an object in orbit around a celestial body.
Kepler's Laws: Laws that describe the motion of planets around the sun, based on observations made by Johannes Kepler in the 1600s.
Newton's Laws of Motion: Laws that describe the relationships between an object's mass, acceleration, and force, and how they apply to the motion of objects in space.
Gravitational Forces: The force of attraction between two objects, such as planets or stars, due to their mass and the distance between them.
Orbital Elements: Mathematical parameters used to describe an object's orbit, including its eccentricity, inclination, and semi-major axis.
Circular and Elliptical Orbits: Two types of orbits that objects in space can follow, with circular orbits having a constant distance from the center of mass of the system, and elliptical orbits having a varying distance.
Astrodynamic Equations: Equations that describe the motion of objects in space, including the vis-viva equation.
Keplerian Orbits: A specific type of orbit that follows Kepler's Laws, with the orbiting object moving along an ellipse with one of the foci at the center of mass of the system.
Orbital Maneuvers: Changes to an object's orbit, often achieved by using a rocket engine to change the object's velocity or direction.
Interplanetary Trajectories: The paths taken by spacecraft as they travel between different planets or other celestial bodies.
Orbital Perturbations: Changes to an object's orbit caused by external factors, such as gravitational forces from other objects or the effects of atmospheric drag.
Escape Velocity: The first type is used to calculate the escape velocity needed by a spacecraft to leave the gravitational pull of a massive body, such as a planet or moon. This equation states that the escape velocity is equal to the square root of two times the gravitational constant times the mass of the planet or moon divided by the radius of the planet or moon.
Velocity in an Elliptical Orbit: The second type of vis-viva equation is used to calculate the velocity of an object in an elliptical orbit around a massive body. This equation states that the velocity is equal to the square root of the gravitational constant times the mass of the planet or moon divided by the semi-major axis of the ellipse, multiplied by the difference between two values: one minus the eccentricity of the orbit, and one plus the radius of the planet or moon divided by the semi-major axis of the ellipse.
"It is the direct result of the principle of conservation of mechanical energy."
"It applies when the only force acting on an object is its own weight, which is the gravitational force."
"The gravitational force is determined by the product of the mass of the object and the strength of the surrounding gravitational field."
"Vis viva (Latin for 'living force') is a term from the history of mechanics..."
"It survives in this sole context."
"It represents the principle that the difference between the total work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done."
"The vis-viva equation quantifies the difference in work done by accelerating and retarding forces in a system."
"The vis-viva equation is one of the equations that model the motion of orbiting bodies."
"The vis-viva equation is a direct result of the principle of conservation of mechanical energy."
"The only force considered in the vis-viva equation is the gravitational force due to the object's own weight."
"The strength of the gravitational force is determined by the mass of the object and the strength of the surrounding gravitational field."
"The difference between the total work of the accelerating forces of a system and that of the retarding forces."
"The difference in work done by the forces is equal to one-half the vis viva accumulated or lost in the system while the work is being done."
"Vis viva is a term from the history of mechanics."
"The vis-viva equation is also referred to as orbital-energy-invariance law."
"The underlying concept is the conservation of mechanical energy."
"Yes, the vis-viva equation specifically models the motion of orbiting bodies."
"The gravitational force is the sole force considered in the vis-viva equation."
"During the work, the vis viva is accumulated or lost in the system."