Spiraling Towards the Center: Solving the Orbit Equation

In summary, the conversation discusses solving the orbit equation and reaching a solution of \frac{1}{r} = A \theta +B. However, the speaker is confused about how this equation indicates that the particle will spiral towards the center. They also mention the original, more complex version of the orbit equation and how it relates to the simplified version they have solved.
  • #1
UrbanXrisis
1,196
1
So i solved the orbit equation:

[tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0[/tex]

the solution is:

[tex]\frac{1}{r} = A \theta +B [/tex]

I am supposed to concude that this particle will sprial towards the center but I don't see that through this equation. could someone explain this to me? thanks
 
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  • #3
the original equation is:

[tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} + (1- \frac{ \mu k}{l^2}) \frac{1}{r} =0[/tex]

describing the motion when the effective porential = 0, i get

[tex]\frac{d^2}{d {\theta} ^2} \frac{1}{r} =0[/tex]

so i was wondering how [tex]\frac{1}{r} = A \theta +B [/tex] tells me that I am sprial towards the center?
 

Related to Spiraling Towards the Center: Solving the Orbit Equation

1. What is the orbit equation?

The orbit equation is a mathematical description of the path that an object takes around another object due to gravity. It takes into account the mass of the objects, the distance between them, and their velocities.

2. How is the orbit equation solved?

The orbit equation can be solved using various mathematical techniques, such as calculus or numerical methods. The specific method used depends on the specific scenario and the desired level of accuracy.

3. What factors affect the orbit equation?

The orbit equation is affected by the masses of the objects, the distance between them, and their velocities. It is also influenced by external factors such as other gravitational forces and atmospheric drag.

4. Why is solving the orbit equation important?

Solving the orbit equation is important for understanding the motion of objects in space and predicting their trajectories. It is also crucial for tasks such as spacecraft navigation and satellite positioning.

5. Can the orbit equation be used for any orbit?

Yes, the orbit equation can be used to describe the motion of any orbiting object, from satellites orbiting the Earth to planets orbiting the sun. However, it becomes more complex for more irregular orbits and may require advanced mathematical techniques.

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