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chris529911
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I have a homework problem that involves the equation v=sqrt((g*R^2)/r) I am confused as to where this equation comes from. I know that Vcirc = sqrt((GM)/r) and Vesc = sqrt((2GM)/r)
chris529911 said:a=v^2/r is the equation for the normal component of acceleration
a=GM/r^2 derived from F= GMm/r^2
a satellite orbiting the Earth only has a normal component of acceleration correct ?
chris529911 said:this is the problem. Why can't you just use v^2=GM/r?
The orbital velocity equation, V=sqrt((g*R^2)/r), is used to calculate the velocity required for an object to maintain a stable orbit around a larger body, such as a planet or star. It is derived from Kepler's third law of planetary motion, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit.
The variable V represents the orbital velocity, g represents the gravitational constant, R represents the radius of the larger body (e.g. planet), and r represents the distance between the two bodies (e.g. distance between the planet and its satellite).
The orbital velocity equation is used in various fields, such as astronomy, astrophysics, and aerospace engineering. It is used to calculate the necessary speed for spacecraft to enter and maintain orbits around planets or other celestial bodies. It is also used in the study and prediction of planetary motion and the behavior of satellites and other objects in orbit.
The orbital velocity equation assumes that the orbiting object is moving in a perfect, circular orbit around the larger body. In reality, orbits are often elliptical and influenced by other factors such as atmospheric drag and gravitational perturbations from other objects. Additionally, the equation does not take into account the mass or size of the orbiting object, which can also affect the orbital velocity.
Yes, the orbital velocity equation can be used for objects orbiting any type of body, as long as the assumptions mentioned above are met. It is commonly used for objects orbiting planets, moons, and stars, but can also be applied to artificial satellites orbiting Earth or other planets, as well as comets and asteroids orbiting the Sun.