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radius-vector

The anomaly is then the angle BFP which the radius vector makes with the major axis.

Let P, P' be two consecutive positions of the radius vector.

From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

Tait that a similar representation of the type (30) is obtained if we replace the circle by an equiangular spiral described, with a constant angular velocity about the pole, in the direction of diminishing radius vector.

Hence equal areas are swept over by the radius vector in equal times.

where h is constant; this shows (again) that the radius vector sweeps over equal areas in equal times.

If p be the radius-vector 0J of the momental ellipsoid Ax+By+Czf=Me4 (I)

The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.

Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the ordinate PR of the traced curve.

In the case of the satellites it is the period relative to the radius vector from the sun.

The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

The co-ordinates of P will then be the following three quantities: - (I) The length of the line OP, or the distance of the body from the origin, which distance is called the radius vector of the body.

(2) The angle XOQ which the projection of the radius vector upon the fundamental plane makes with the initial line OX.

(3) The angle QOP, which the radius vector makes with the fundamental plane.

r, the distance apart of the two bodies, or the radius vector of m relative to M.

The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.

The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.

Taking as the radius vector of each body the line from the body to the common centre of gravity of all, the sum of the products formed by multiplying each area described, by the mass of the body, remains a constant.

The speed of the latter may, therefore, be expressed as a function of its radius vector at the moment and of the major axis of its orbit without introducing any other elements into the expression.

Hansen, therefore, shows how the radius vector is corrected so as to give that of the true planet.

This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

Of the three co-ordinates,the radius vector does not admit of direct measurement, and must be inferred by a combination of indirect measurements and physical theories.

As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet.

The anomaly is then the angle BFP which the radius vector makes with the major axis.

P is the position of the planet at any time, and we call r the radius vector FP. The angle AFP between the pericentre and the position P of the planet is the anomaly called v.

Let P, P' be two consecutive positions of the radius vector.

From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

Tait that a similar representation of the type (30) is obtained if we replace the circle by an equiangular spiral described, with a constant angular velocity about the pole, in the direction of diminishing radius vector.

Hence equal areas are swept over by the radius vector in equal times.

where h is constant; this shows (again) that the radius vector sweeps over equal areas in equal times.

If p be the radius-vector 0J of the momental ellipsoid Ax+By+Czf=Me4 (I)

The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.

Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the ordinate PR of the traced curve.

In the case of the satellites it is the period relative to the radius vector from the sun.

The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

The co-ordinates of P will then be the following three quantities: - (I) The length of the line OP, or the distance of the body from the origin, which distance is called the radius vector of the body.

(2) The angle XOQ which the projection of the radius vector upon the fundamental plane makes with the initial line OX.

(3) The angle QOP, which the radius vector makes with the fundamental plane.

r, the distance apart of the two bodies, or the radius vector of m relative to M.

The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.

The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.

Taking as the radius vector of each body the line from the body to the common centre of gravity of all, the sum of the products formed by multiplying each area described, by the mass of the body, remains a constant.

The speed of the latter may, therefore, be expressed as a function of its radius vector at the moment and of the major axis of its orbit without introducing any other elements into the expression.

Hansen, therefore, shows how the radius vector is corrected so as to give that of the true planet.

This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

Of the three co-ordinates,the radius vector does not admit of direct measurement, and must be inferred by a combination of indirect measurements and physical theories.

As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet.

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.