Dynamics Apse and Apsidal Distance
- 1. Ms. M. Mohanamalar, M.Sc., M.Phil., Ms. N. Malathi, M.Sc., DYNAMICS (18UMTC41) II B.Sc. Mathematics (SF)
- 2. Apse and Apsidal Distance
- 3. In mechanics, either of the two points of an orbit which are nearest to and farthest from the centre of motion. They are called the lower or nearer, and the higher or more distant apsides respectively. The "line of apsides" is that which joins them, forming the major axis of the orbit. The length of the line of apsides is called the apsidal distance
- 4. If there is a point A on a central orbit at which the velocity of the particle is perpendicular to the radius OA, then the point A is called an Apse and the length OA is the corresponding apsidal distance. Hence at an apse, the particle is moving at right angles to the radius vector.
- 5. We know that where u = , r being the distance from the centre of force and p is the perpendicular from the centre of force upon the tangent. At an apse, p = r = . Hence from the above relation we get = 0 at an apse.
- 6. Here we consider the problems namely given the value of the central acceleration P, we will find the path. We use the (u,) equation To solve this differential equation, we multiply both sides by 2 , we get
- 7. Hence we get Integrating both sides with respect to ,