# Motion Of Sattelite around the earth

How does the Satellites are made to move exactly in circular orbit around the earth?
how many forces are used? what is their value?

Well, the orbits aren’t usually perfectly circular, and the forces at play are the acceleration of the rocket that launched the satellite and the gravity of Earth that keeps trying to pull it back.

Is this one of those “how is skylabby formed?” questions?

You (the OP that is) might want to Google on “orbit insertion”, which is the term for this process.

After a cursory look around for some hard data, I found these figures on the insertion of the Venus Express satellite into orbit around Venus, back in 2006. You’ll notice it takes several steps (changes in momentum) to do it.

The satellite is trying to fall and failing. It also has rockets on board to help it stay aloft, but mainly it’s simply failing to fall.

The secret is conservation of momentum, meaning that something going in a specific direction won’t just suddenly stop going in that direction unless it hits a wall sufficient to stop it or some other force acts on it. The forces of interest here are those imparted to the satellite when it was launched, which got it moving in a sideways direction relative to the Earth, and gravity, which constantly acts on it to drag it down towards the center of the Earth.

So, every single instant, our simplified satellite has two forces acting on it at right angles to each other: The force from the launch, which points sideways, and the force of gravity, which points down. Each instant, the sideways force nudges it to one side and the downwards force nudges it down. Adding these forces together, you get a single nudge at a 45 degree angle, which agrees with the orbit the satellite actually takes.

Now, you may object, and say the satellite doesn’t move in piecewise steps, but instead travels fluidly through free space and in our model you’d be right. The answer to this is what Newton and Leibniz found out, the idea of slicing your moments of time thinner and thinner until, out at the far limit, you have smooth motion and curved lines. That is the fundamental idea of the Calculus, discredited for too long until Nonstandard Analysis brought it back into favor.

1. Almost NO satellite moves in a circular orbit “exactly.” They all have at least a slight eccentricity to the orbit, sometimes a very large eccentricity, usually for some specific purpose.

2. The only “force” involved is the Earth’s gravity, (32 feet per second per second [9.81 meters per second per second] at the surface, dropping off gradually as the distance increases by the “Inverse Square” of the distance.) It is a function of the Gravitational Constant, G.

What keeps a satellite in orbit is its velocity. For an object in Low Earth Orbit(LEO), generally defined as less than 2000, and more than 200 kilometers above the surface of the Earth, the orbital velocity is 6.9 to 7.8 kilometers per second for a roughly circular orbit, the higher number at the lower altitude. An object in Low Earth Orbit takes from 89 to 128 minutes to complete one revolution around the Earth.

Satellites, Shuttles, the ISS and any other object “in orbit” is in free fallaround the more massive body. This means there are no other forces, besides gravity, affecting the orbiting object.

A Geostationary Orbitis at an altitude of 35,786 km (22,236 mi) above the Earth’s surface, and moving at a speed of 3.1 kilometers per second, the satellite takes exactly one day to complete its orbit. Those satellites are in a very nearly circular orbit, almost directly above the equator, and appear to be “fixed” in one location with respect to the surface.

If you observe a geostationary satellite closely with a telescope, you would notice it usually makes a small “figure eight” in the sky, since the orbit is almost certainly not exactly circular, and is almost certainly not exactly above the equator. This means that when its altitude is slightly lower, its speed is greater, and it moves a bit “ahead” of its average location. At the other end of its orbital path, it is higher, moving slower, and is slightly “behind” its average location.

Due to the orbit being slightly tilted with respect to the equator, sometimes the satellite is North of its average position, and other times it is slightly South of that position.

The combination of these effects produces the “figure eight”.

Basically you just need to get it moving sideways fast enough so that when it falls back to Earth, it misses. The higher up it is, the slower this needs to be, since a slower movement at a greater distance misses the ground just as well as a fast speed at a lower height.

Hope this helps.

Here’s my simplified version of what Derleth and DrFidelius are trying to say:

The satellite IS falling. But it is moving forward so fast that by the time it has fallen any distance at all, the curvature of the earth matches it by the same distance. In other words, in the time it takes the satellite to fall 50 feet, the surface of the earth is about 50 feet further away. The result is that the satellite keeps falling and falling and falling and never hits bottom.

Read Douglass Adams’ description of how to fly-- That’s actually a pretty good layman’s explanation of an orbit.

I’ll just point out, though, that a satellite in orbit has no forces acting on it whatsoever, and therefore moves in the closest thing you can get to a straight line.

Well, it’s failing to land. The falling part it actually seems to keep on doing pretty well.

I’m sure there’s a typo in here somewhere. What about gravity?

I’ll concede that an object moving from one galaxy to another, and very far from any such area will have negligible forces acting on it, but not one which in orbit around an identifiable body.

I think he maybe referring to general relitivity version of gravity in which things in a gravitational field move in straight lines, but the space is curved.

This is partially right, but in the context of the original post, it may be confusing. Conservation of Momentumis the assertion that an object in motion will remain in motion, at its current speed and direction (velocity) unless acted on by an external, unbalanced force. This is related to the property of Inertia.

Conservation of Momentum, or Inertia, is not properly considered a Force, and cannot be used in calculations as if it were. The highlighted sections of the quote are misleading, as they suppose that inertia can be added as an element in the force parallelogram to resolve a net force.

Once the boost phase of the launch has completed, the force “imparted to the satellite when it was launched” has terminated, and the rocket, or satellite, is now moving ballistically, in the sense that the orbital vehicle is no longer actively accelerating. It is true that many orbiting systems have small thrusters to boost them to a higher orbit, but these are not used continuously to power the vehicle in orbit.

Due to many factors, Orbital Spaceflightis a complex ballet of systems and energy balance. In Low Earth Orbit, the tenuous upper atmosphere is enough to produce a significant drag on the orbiting satellite, causing it to lose energy and move to a lower altitude, where, eventually, the thicker atmosphere will cause it to “de-orbit” and burn up on re-entry to the Earth. The pressure of Solar wind particles is also involved, more so for higher-altitude orbits.

To forestall these effects, in Orbital Station-Keeping, small thrusters are employed to periodically boost the orbital vehicle to a higher orbit, and maintain the position of the satellite to whatever degree is appropriate for its mission.

While the forces of drag, and thrusters, has an effect on the overall orbit, in the context of the OP, the only relevant Force (defined as “Causing an Acceleration, or change in Velocity”) is Gravity.

I’m pretty sure Chronos is talking about General Relativity, where gravity is defined as a warping of space-time, making the curved (to outsiders) path of an orbit something that’s locally a straight line. In Newtonian mechanics, which is the mental model most well-educated people who aren’t physicists grasp fairly well, gravity is indeed a force much like, say, magnetism is a force, but that comes to grief when we try to take it the rest of the way and integrate gravity into our quantum field theories.

DHMO: You’re obviously correct. I still think my mental model is easier to picture, but perhaps there I simplified a bit too far.

I still like the cannonball explanation.

Imagine a cannon, pointed sideways, on top of a huge mountain. (And ignore air resistance and friction, for the moment.) If you shoot the cannon, the cannonball will come out and follow a curved path until it hits the ground. Shoot the cannonball faster and it will even go over the distant horizon before striking the Earth. Shoot it fast enough and it will be continuously going over the horizon; curving toward the Earth, but never so much that it hits it. That’s orbit.

Of course we don’t put things in orbit with cannons, we use rockets. Program the rocket correctly and you can put the satellite wherever you want it; low, high, north, south, wherever[sup]*[/sup]. If you put one over the equator, moving due east, and at just the right speed and altitude, it’ll take 24 hours to go around. It appears to just be floating in space. The reality is more like two planes flying in formation; moving together so that each sees the other as standing still.

• The real world imposes certain constraints. And remember, you have to go around the Earth, can’t just hover over the North Pole, for example.

Mr. Newton was fond of it also.