orbital motion

• An artificial satellite is a man-made body placed in orbit around the earth or another planet to collect information about it or communicate. The International Space Station is an example of an artificial satellite.
• Artificial satellites orbiting the Earth are a familiar part of modern technology.
• A circular orbit is the simplest case. Circular orbital motion is when an object moves in a circular path around the center of mass of a system.
• The only force acting on a satellite in a circular orbit around the earth is the earth’s gravitational attraction, which is directed toward the center of the earth and hence toward the center of the orbit.
• This means that the satellite is in uniform circular motion and its speed is constant.
• The satellite isn’t falling toward the earth; rather, it’s constantly falling around the earth. In a circular orbit, the speed is just right to keep the distance from the satellite to the center of the earth constant.
• In a circular orbit, the following quantities are constant: distance, speed, angular speed, and potential and kinetic energy.
• Earth’s actual: Mass = 5.972x10^24 kgs radius = 6.38 x10^6 m
• Gravitational force. Note: Fg = Fc (centripetal force) Fg = G Mm / r^2 where; Fg = gravitational force G = gravitational constant M = mass of the Earth m = mass of the satellite
• Radial acceleration -acceleration of the satellite arad = mv^2 / r where; arad = radial acceleration m = mass v = velocity r = radius
• Formula = arad Note: (m) or mass in the a rad equation will be diminished or removed because the orbital motion of the satellite does not depend on its mass.
• v= √Gm/r

  This relationship shows that we can’t choose the orbit radius r and the speed independently; for a given radius r, the speed for a circular orbit is determined
• The satellite’s mass (m) doesn’t appear in the equation above, which shows that the motion of a satellite does not depend on its mass. If we could cut a satellite in half without changing its speed, each half would continue on with the original motion.
• T = 2πr/v