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[Q] Elliptical orbit


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The moon does indeed orbit the Earth in an elliptical orbit. Or more precisely, both the Earth and the moon orbit their common center of gravity.

 

Orbit of the Moon - Wikipedia, the free encyclopedia

 

Also, even if the orbit was perfectly circular, I don't think it would be inappropriate to view this as a specific case of an elliptical orbit where F1 and F2 from the diagram of an ellipse below are located in the same spot, giving an orbit of zero eccentricity.

 

 

For more information on basic planetary motion, check out Kepler's laws of planetary motion - Wikipedia, the free encyclopedia

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The moon does indeed orbit the Earth in an elliptical orbit. Or more precisely, both the Earth and the moon orbit their common center of gravity.

 

Orbit of the Moon - Wikipedia, the free encyclopedia

 

Also, even if the orbit was perfectly circular, I don't think it would be inappropriate to view this as a specific case of an elliptical orbit where F1 and F2 from the diagram of an ellipse below are located in the same spot, giving an orbit of zero eccentricity.

 

 

 

For more information on basic planetary motion, check out Kepler's laws of planetary motion - Wikipedia, the free encyclopedia

 

I 'think' I get it but not being a mathematician or even a scientist, I can only use an analogy to explain it to myself. There seems to be to me from the explanation, two forces in operation - one that holds the body in orbit, like two children with linked hands, swinging in circles (attraction/ gravity) and the other being like something caught in a vortex in a river, which swings it out on an eccentric orbit as it tries to escape this control, giving it this ellipse? :hyper:

 

I base this assumption based on the Wiki 'Two Body Problem' diagram and write up, plus the discussion link below.:agree:

 

the specific orbital energy formulas apply, with specific potential and kinetic energy and their sum taken as the totals for the system, divided by the reduced mass; the kinetic energy of the smaller body is larger; the potential energy of the whole system is equal to the potential energy of one body with respect to the other, i.e. minus the energy needed to escape the other if the other is kept in a fixed position; this should not be confused with the smaller amount of energy one body needs to escape, if the other body moves away also, in the opposite direction: in that case the total energy the two need to escape each other is the same as the aforementioned amount; the conservation of energy for each mass means that an increase of kinetic energy is accompanied by a decrease of potential energy, which is for each mass the inner product of the force and the change in position relative to the barycenter, not relative to the other mass

 

If I'm wrong, please correct me with an analogy or another link, for more detail.

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I am not the right person to answer your question, but hopefully someone will correct me and we will both learn something along the way.

 

If I understand your question correctly- you do not understand why all things don't orbit in circles, or why there are different eccentricities of orbits. There are two forces acting upon an orbiting body. 1) the gravitational pull of both bodies to each other in a straight line and 2) The orbiting body's velocity which is at a right angle to the force of gravity. The simplest analogy is swinging a weight around on a string. Gravity is represented by the string and provides the centripetal force that keeps the weight "orbiting" your hand, rather than flying off in one direction. In this case, both forces are equal, and at right angles to each other, so you end up with a peferctly circular "orbit". Imagine another instance where instead of a string, you use a long rubber band. Now, instead of smoothly rotating the weight around, wip it around in one direction. You will end up with an "orbit" with extreme eccentricity. The velocity of the orbiting body increases at it approaches the body it is orbiting, and decreases as it is moving away because of conservation of angular momentum. There is nothing about gravitational interaction that dictates circular orbits. A circular orbit is just one special instance of an elliptical orbit where eccentricity is zero.

 

I recommend digging through the hyperphysics site, specifically the areas dealing with orbits

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I am not the right person to answer your question, but hopefully someone will correct me and we will both learn something along the way.

 

If I understand your question correctly- you do not understand why all things don't orbit in circles, or why there are different eccentricities of orbits. There are two forces acting upon an orbiting body. 1) the gravitational pull of both bodies to each other in a straight line and 2) The orbiting body's velocity which is at a right angle to the force of gravity. The simplest analogy is swinging a weight around on a string. Gravity is represented by the string and provides the centripetal force that keeps the weight "orbiting" your hand, rather than flying off in one direction. In this case, both forces are equal, and at right angles to each other, so you end up with a perfectly circular "orbit". Imagine another instance where instead of a string, you use a long rubber band. Now, instead of smoothly rotating the weight around, whip it around in one direction. You will end up with an "orbit" with extreme eccentricity. The velocity of the orbiting body increases at it approaches the body it is orbiting, and decreases as it is moving away because of conservation of angular momentum. There is nothing about gravitational interaction that dictates circular orbits. A circular orbit is just one special instance of an elliptical orbit where eccentricity is zero.

 

I recommend digging through the hyperphysics site, specifically the areas dealing with orbits

 

I thought of the string analogy but that is why I questioned the elliptical orbit. It seemed that if the pull of gravity was constant, then it should be circular. The rubber band analogy is good though because if you tie a weight to it and fire it off, it swings back and forth, not goes round in a circle, suggesting to me a captured orbit of objects, not that I know anything because like you I'm just a layman trying to make sense of the phenomena.

 

Will look up the hyperphysics site or put this thing to bed, at least on my side, depending if it inspires me further or not.:thanks:

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I 'think' I get it but not being a mathematician or even a scientist, I can only use an analogy to explain it to myself.
OK imagine yourself on a roller-coaster ride.

 

As your cart goes up, you get slower and slower. When it goes over the top and heads back down, you get faster and faster. Going up and down just mean further and nearer to the centre of the earth. The same happens with a thrown stone, but without the tracks guiding it, its course is determined only by gravity and its velocity and perhaps the wind.

 

In the case of the moon, only gravity and velocity come into the game. If it had insufficient tangential velocity it would eventually fall straight toward the earth, just like the stone thrown upward. That is radial velocity. The moons tangent velocity would have it going away, but gravity deviates its velocity and curves its course. When it is at the apogee it has less velocity and, even though this velocity is purely tangent there, it isn't enough to maintain that distance and gravity prevails. At perigee at has more velocity and this prevails over gravity.

 

To have a circular orbit you have to give the rock a purely tangent velocity with the right magnitude for the strength of gravity at its radius and for the radius itself. If you start it at the same position and direction but with a smidgen less speed, that point will be the apogee of an eliptic orbit, with a smidgen more speed it wil be the perigee. Of course, how much more or less speed determines how much the elipse will differ from the circle.

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OK imagine yourself on a roller-coaster ride.

 

As your cart goes up, you get slower and slower. When it goes over the top and heads back down, you get faster and faster. Going up and down just mean further and nearer to the centre of the earth. The same happens with a thrown stone, but without the tracks guiding it, its course is determined only by gravity and its velocity and perhaps the wind.

 

In the case of the moon, only gravity and velocity come into the game. If it had insufficient tangential velocity it would eventually fall straight toward the earth, just like the stone thrown upward. That is radial velocity. The moons tangent velocity would have it going away, but gravity deviates its velocity and curves its course. When it is at the apogee it has less velocity and, even though this velocity is purely tangent there, it isn't enough to maintain that distance and gravity prevails. At perigee at has more velocity and this prevails over gravity.

 

To have a circular orbit you have to give the rock a purely tangent velocity with the right magnitude for the strength of gravity at its radius and for the radius itself. If you start it at the same position and direction but with a smidgen less speed, that point will be the apogee of an eliptic orbit, with a smidgen more speed it wil be the perigee. Of course, how much more or less speed determines how much the elipse will differ from the circle.

 

Nice answer! It's funny but when I first thought of this idea, I thought it be a dud as with most of my (mostly unanswered) questions. It has instead turned out to be quite interesting and I'm glad I asked as it has given me more of an angle on the phenomena than say 'The Slit Experiment' whose results I still can't fathom!

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  • 1 month later...

Phenomena in mechanics are usually explained by relative frames of reference. In this, a point in space or a reference body is assumed as stationary and movements of all (other) bodies are measured/determined with respect to this static reference. A displacement of reference point/body or an action on it is automatically assigned to referred-bodies instead of to the reference-body. These types of explanations have the advantage of simplicity and they give accurate results for relative positions of referred-bodies.

Yet, these results are apparent and could be true only in cases to find relative positions of concerned bodies. By assuming the reference-body to be stationary and taking relative motions of referred-bodies as true facts, we greatly alter parameters of these bodies. Use of these altered parameters to determine physical actions by/on bodies, resulting parameters of bodies or shape of their paths will be incorrect.

Sun (central body) is a moving body. We get circular/elliptical shapes of planetary orbital paths only when the sun is assumed as a static body. These structures are unreal and they can be used only to determine relative positions of planets with the sun. Movement, rotation, precession, etc. are physical actions and they are restricted to physical (real) bodies. Apparent orbit of a planet, being only an imaginary structure, it cannot move, rotate or precess. As long as the sun (or any central body) is moving, no planetary body can orbit around it in a geometrically closed real path.

No free body (other than galaxies) can remain stationary in space. Real orbital path of a planetary body is of wavy shape about its moving central body. A planetary body and central body move along a median path around (static) galactic center, planetary body moving periodically to front and rear of the central body. Hence, other than for determination of their relative positions, assumption of orbital paths of planets/satellites as circular/elliptical (closed geometrical) shape is not right.

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Just to be detailed, galaxies are not static in space. For instance, the galaxy we're in is one of the "local group" and they're all moving with regard to each other. Aside from that, there's the issue of the expansion of the universe. Given any collection of objects, there is a centre of mass, which can be taken as the reference point for that group, but any other grouping will have a different centre of mass, likely with a different motion as well.

At the other end of the scale, a thrown stone is in orbit around the earth, but as the orbital path intersects the earth's surface, the stone will not complete an orbit.

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