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Motion of “Two body” system is the elementary unit of motion of heavenly bodies.

“Two body” system represents the starting point for studying motion of celestial bodies, including Earth. In general, gravitational force is dominant for a pair of masses in such a manner that influence of all other bodies can be neglected as first approximation. In that case, we are left with an isolated “two body” system. The most important deduction of this simplifying assumption is that isolated system is free of external force. This means that “center of mass” of the isolated system in not accelerated.

In the solar system, one of the massive bodies is Sun and the other is one of the planets. In this case, Sun is relatively much larger than second body. Similarly, in Earth-moon system, Earth is relatively much larger than moon. On the other hand, bodies are of similar mass in a “binary stars” system. There are indeed various possibilities. However, we first need to understand the basics of the motion of isolated two bodies system, which is interacted by internal force of attraction due to gravitation. Specially, how do they hold themselves in space?

In this module, we shall apply laws of mechanics, which are based on Newton’s laws of motion and Newton's law of gravitation. Most characterizing aspect of the motion is that two bodies, in question, move in a single plane, which contains their center of mass. What it means that the motion of two body system is coplanar.

Two body system

The plane of "one body and center of mass" and plane of "other body and center of mass" are in the same plane.

Newtonian mechanics provides a general solution in terms of trajectory of a conic section with different eccentricity. The trajectories like linear, circular, elliptical, parabolic, hyperbolic etc are subsets of this general solution with specific eccentricity. Here, we do not seek mathematical derivation of generalized solution of the motion. Rather, we want to introduce simpler trajectories like that of a straight line, circle etc. first and then interpret elliptical trajectory with simplifying assumptions. In this module, we shall limit ourselves to the motion of “two body” system along a straight line. We shall take up circular motion in the next module.

In a way, the discussion of motion of “two body” system is preparatory before studying Kepler’s laws of planetary motion, which deals with specific case of elliptical trajectory.

The general solution of two bodies system involves polar coordinates (as it suits the situation), vector algebra and calculus. In this module, however, we have retained rectangular coordinates for the most part with scalar derivation and limited our discussion to specific case of linear trajectory.

Straight line trajectory

This is simplest motion possible for "two body" system. The bodies under consideration are initially at rest. In this case, center of mass of two bodies is a specific point in the given reference. Also, it is to be noted that center of mass lies always between two bodies and not beyond them.

Questions & Answers

List the application of projectile
Luther Reply
How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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