James Brady said:I'm trying to figure out how to calculate the velocity of an orbit at apogee or perigee and I've figured out the derivation of the equation except for this one fraction... I replaced the radius quantities for x and y for ease of viewing.
[itex]\frac{x-y}{x^2 - y^2} = \frac{1}{x + y}[/itex]
Can anybody break this down for me barney-style?
To solve for the velocity of an orbit, you need to know the mass of the central body, the radius of the orbit, and the gravitational constant. You can use the equation v = √(GM/r) to calculate the velocity, where G is the gravitational constant, M is the mass of the central body, and r is the radius of the orbit.
The gravitational constant, denoted by G, is a fundamental constant used in the calculation of gravitational forces between two objects. It has a value of approximately 6.674 x 10^-11 m^3kg^-1s^-2.
The mass of the central body has a direct effect on the velocity of an orbit. The larger the mass of the central body, the greater the gravitational force and therefore the higher the orbital velocity required to maintain the orbit.
If the radius of an orbit increases, the velocity required to maintain the orbit decreases. This is because the gravitational force decreases with distance, so a larger radius requires a lower velocity to balance the gravitational force.
No, the velocity of an orbit cannot be negative. The velocity of an orbit is always positive and determines the direction of the orbit (clockwise or counterclockwise). Negative velocity would indicate a reversal of the orbit, which is not possible in a stable orbit.