<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The satellite is in fact following a geodesic in curved space-time and is not influenced by any outside forces. No, I'm not rejecting the new interpretation of circular motion. I'm wondering why this dual interpretations of circular motion produce the same result? If you use moon's mass and its speed around the earth and use "gravity=centripetal" formula, you'll get a earth-moon distance of 240000miles. If you use mass of earth and its speed around the sun, and use the above equality, you'll again get a sun-earth distance of 93000000 miles. It goes on and on... If a satellite is 'free falling', IMO, that's because it can't keep a constant speed for various reasons.</DIV></p><p>They produce the same result because they are describing the same phenomenon. Both Newton's theory of mechanics and of gravity and general relativity are accurate within their domains of validity. It is just that general relativity is accurate over a broader range of circumstances. In circumstances in which gravitational fields are modest (they almost always are except in rare circumstances like black holes) and in which speeds are small compared to the speed of light, general relativity and Newton's theory agree very very closely. General relativity is a little bit more accurate, but not enough to notice for most practical considerations.</p><p>But what is going on is relatively simple. Let's neglect the drag that occurs from a very thin atmosphere in space, solar wind and other tiny effects. In a vacuum satellites do in fact maintain a constant speed. What they don't maintain is a constant velocity, and the difference is important. Speed is a measure of how fast something moves, and it does not matter what the directin of motion is. So a race car speeding around a circular track can do so at constant speed. But velocity is a vector and measures not only speed but also the direction of motion. If the direction changes then so does the velocity, even if the speed is constant. So a race car going around the track at Indy at a constant speed of 200 mph is also changing velocity constantly because the direction changes.</p><p>Now Newton's equation for a body of constant mass, F = ma tells us that force is equal to mass x acceleration. Acceleration is a change in velocity, not necessarily a change in speed. The driver of the race car traveling around the track at Indy, feels the car pushing on him towards the center of the track, and the car "feels" a similar force due to friction between the tires and the pavement. That force, directed towards the center of the track is the result of the change in direction of his motion. In the case of the Earth revolving around the sun, the force comes from gravity. Similarly in the case of a satellite orbiting the Earth. The speed of the Earth and the speed of the satellite are constant (I have idealized this to the case of a circular orbit, for an elliptical orbit the speed also changes a little bit as the satellite gets closer and farther from the Earth, just like going up and down hills). What changes is the direction of motion as the satellite describes a circular path. And what is happening to maintain an orbit is that as the satellite "falls" it also has a tangential component of velocity that causes it to curve outward from the center of the Earth, and it literally falls around the Earth.</p><p>"Centrifugal force" and "centripetal force" are examples of unfortunate terminology. They often serve to confuse rather than elighten. They are not really forces at all, but are simply the result of Newtonian mechanics and changes in the direction of motion, even when speed is constant. </p><p> [Long time ago I read somewhere, I'm not sure if it is true, that NASA still use Newtonian gravitation and mechanics for their space flights instead of more 'accurate' Einstein's relativity. Btw, in good old mechanics, the force used against gravity is called 'centrifugal force', away from the center. <br />Posted by emperor_of_localgroup</DIV></p><p>Think about the situation of a satellite. There is nothing whatever acting on the satellite to pull it away from the center of the Earth. No strings, no electromagnetic forces, nothing. Gravity is pulling the other way. The ONLY force involved is gravity. </p><p>Everybody uses Newtonian mechanics for almost all applications. There is nothing special about NASA in that regard. That is because it is sufficiently accurate for most things. It is certainly sufficiently accurate for calculating the orbits of satellites. In fact even in many astrophysical models, say the motion of galaxies about one another, Newtonian mechanics is used. It is far far easier to perform the calculations to solve Newton's equations than it is to solve the Einstein equations in most situations. And they work just fine for most things.</p><p>Orbital mechanics models for the solar system and such rely exclusively on Newtonian mechanics, and often on approximations to Newtonian mechanics at that. Quite a few models look at only two bodies at a time and put together trajectories using patched conics. It turns out to actually be a bit difficult to model the interactions among three or more bodies, even in a Newtonian setting. In fact there are no close form solutions for three or more bodies and one must rely on simulations. The problem would be even more difficult, and not more enlightening, if formulated in terms of general relativity.</p><p>You only need general relativity if the speeds are an appreciable fraction of the speed of light, if gravitational fields are extremely high, or if you need an extraordinary degree of accuracy. For most purposes Newtonian gravity suffices. <br /></p> <div class="Discussion_UserSignature"> </div>