Find equation of path of a point mass under influence of 2 central forces

In summary, taureau20 was not able to solve the equation of path for a point mass under the influence of two central forces. He was able to post his attempt at doing so, but needs help understanding the equations. He asks for help with understanding the tags needed to post his equations in LaTeX format.
  • #1
taureau20
9
0
A point mass ‘A’ is kept at the origin. Another B is kept at the x-axis at x = H. Another C is kept at distance H from origin and distance h from B. A, B and C thus form an isosceles triangle with vertex A. Given that A's mass >> B's mass >> C's mass; Newton’s gravitational law governs the bodies. C will have motion because of both A and B while B will have motion because of A only.
Find:
The equation of path of C in any coordinate system given that B and C have zero initial velocities.
 
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  • #2
Welcome to PF!

Hi taureau20! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
  • #3
tell me within what tags must I enclose the LATEX code so I can post mathematuical expressions here. I can't do that here. Plz help w.r.t. that.

anyway, you may click http://www.physicshelpforum.com/phy...urce-one-stationary-one-moving.html#post1534"; in this site, the LATEX coding has worked so I have posted my attempt at solving this problem.

You can take it from there!

Thanks!
 
Last edited by a moderator:
  • #4
taureau20 said:
tell me within what tags must I enclose the LATEX code so I can post mathematuical expressions here. I can't do that here. Plz help w.r.t. that.

anyway, you may click http://www.physicshelpforum.com/phy...urce-one-stationary-one-moving.html#post1534"; in this site, the LATEX coding has worked so I have posted my attempt at solving this problem.

You can take it from there!

Thanks!

Hi taureau20! :smile:

sorry, but I can't follow your equations (3) and (4) :confused:

is theta measured from B or from C?

why is there no ka in (3)?

Can you check it, and type it out again, here … for LaTeX in this forum, just type [noparse][tex] before and [/tex] after.[/noparse] :smile:
 
Last edited by a moderator:

1. What is a central force?

A central force is a type of force that acts on an object towards a single, fixed point called the center of force. Examples of central forces include gravity, electrostatic forces, and magnetic forces.

2. How do central forces affect the motion of a point mass?

Central forces cause a point mass to move in a curved path around the center of force. This path is known as the trajectory or orbit. The shape of the trajectory depends on the strength and direction of the central force.

3. What are the key factors in determining the equation of the path of a point mass under the influence of two central forces?

The key factors are the masses of the objects exerting the central forces, the distance between them, and the strength and direction of the two central forces. These factors can be described using mathematical equations, such as Newton's Law of Universal Gravitation.

4. Can the equation of the path of a point mass under the influence of two central forces be solved analytically?

In most cases, the equation of the path cannot be solved analytically. However, it can be approximated using numerical methods or simplified models. In some special cases where the central forces have specific properties, the equation can be solved analytically.

5. How is the equation of the path of a point mass under the influence of two central forces used in real-world applications?

The equation of the path is used in various fields of science and engineering, such as celestial mechanics, aerospace engineering, and astrophysics. It helps us understand and predict the motion of objects in space, such as planets, satellites, and comets. It also plays a crucial role in designing and controlling spacecraft trajectories.

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