Speed Of Satellite Orbiting Earth Equation

Spreadsheet uses 6 674e 11 m3 kg sec2 5 972e 24 kg 6437e 06 m.

Speed of satellite orbiting earth equation. Suspect the difference may be the result of different values used for g m earth and radius earth. In gravitationally bound systems the orbital speed of an astronomical body or object e g. Around the sun orbital speed of the earth is 108 000 km h. Since earth also rotates once in 24 hours a satellite at 22 223 miles altitude stays in a fixed position.

Assuming a circular orbit we equate the centripetal force to the force of gravity for a stable orbit. We have done the hard part and found equations 5 and 8 which describe the evolution of the sun earth system over time. Just as in the case of the motion of projectiles on earth the mass of the projectile has no effect upon the acceleration towards the earth and the speed at any instant. V sqrt frac g m e r does a satellite with a large or small orbital radius have the greater velocity.

M v 2 r g me m r 2. The speed can t vary as long as the satellite has a constant orbital radius that is as long as it s going around in circles. Planet moon artificial satellite spacecraft or star is the speed at which it orbits around either the barycenter or if one object is much more massive than the other bodies in the system its speed relative to the center of mass of the most massive body. My results are slightly different a bit high on orbital altitude and a bit low on velocity.

The period speed and acceleration of a satellite are only dependent upon the radius of orbit and the mass of the central body that the satellite is orbiting. This equation holds for any orbiting object where the attraction is the force of gravity whether it s a human made satellite orbiting the earth or the earth orbiting the sun. Velocity v square root g m r where g is a gravitational constant m is the mass of earth or other larger body and radius is the distance at which the smaller mass object is orbiting. The average speed over an entire orbit or its instantaneous speed at a particular point in its orbit.

The orbital speed formula is provided by where g gravitational constant m mass of the planet r radius. M is mass of satellite v is velocity of satellite r is radius of orbit of satellite g is gravitation constant me is mass of earth. Solving equations of motions with euler s method. Examine the following equation which relates the speed of an orbiting satellite and the distance from the center of earth.

To maintain an orbit that is 22 223 miles 35 786 kilometers above earth the satellite must orbit at a speed of about 7 000 mph 11 300 kph. Simplifying the equation writing in terms of. The formula for orbital speed is the following. The term can be used to refer to either.

The term can be used to refer to either the mean orbital speed i e. Equation 8 will be used in our program to compute the angle θ from its second derivative.