Calculating the Effects of Velocity and Gravity on Orbital Motion

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Discussion Overview

The discussion revolves around the effects of velocity and gravitational acceleration on orbital motion, particularly focusing on how these factors influence an object's trajectory over time. Participants explore the mathematical modeling of these dynamics, including vector addition and the implications of continuous acceleration due to gravity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the initial velocity vector remains relevant after the first second of motion, suggesting that it may not apply if acceleration continues.
  • Another participant asserts that the object's velocity changes continuously due to ongoing gravitational acceleration, indicating that the initial velocity becomes less significant over time.
  • A participant mentions that their modeling in JavaScript yields unrealistic results, implying potential issues with the implementation of gravitational effects in their calculations.
  • There is a suggestion that an orbit can be conceptualized as a continuous fall towards a target, emphasizing the equilibrium nature of orbital motion.
  • One participant inquires about methods to calculate changing velocity, indicating a need for clarity on the mathematical approach to modeling these dynamics.
  • Another participant reiterates the method of calculating changing velocity by adding acceleration vectors at each time step, noting that the influence of the initial velocity diminishes over time.

Areas of Agreement / Disagreement

Participants generally agree that the initial velocity vector does not remain constant if acceleration continues, but there is no consensus on the specifics of how to model this accurately or the implications of the gravitational effects on the velocity over time.

Contextual Notes

Some limitations in the discussion include the potential for missing assumptions regarding the nature of the gravitational force, the specific implementation details in the modeling code, and the mathematical steps involved in calculating changing velocities.

Who May Find This Useful

This discussion may be useful for individuals interested in orbital mechanics, physics simulations, or those looking to understand the mathematical modeling of motion under gravitational influence.

Phys_Boi
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So if an object has a velocity expressed by the vector <-3,0> and is being accelerated toward another object with the vector <-1,-2>... After one second, the object will have moved from (0,0) to (-4,-2) - calculated by adding the vectors.. My question is after the first second does the object keep the initial -3 velocity vector?

I am trying to map orbital motion and have so far been taking the sum of the initial two vectors and adding them to the gravity vector. Then the resulting vector will be added to the new gravity vector and so on...

However, this is getting unrealistic results.. So which vectors are applying to the object?

Does the initial velocity vector always apply to the object or does the vector decrease or does it drop after the first second?

Thank you for any help.
 
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Phys_Boi said:
My question is after the first second does the object keep the initial -3 velocity vector?
No. The object has a new velocity, which you've calculated. The original velocity is no longer relevant. What happens next depends on whether the acceleration continues; if not, the object's velocity will remain at its new value.
 
Thank you for your reply..
Like I said, I'm doing some orbital motion modeling in JavaScript.. The acceleration continues because it is a gravitational acceleration. However, in my program when I do add an initial velocity, it is quickly overtaken by the gravity component in an, almost, unnatural way. Maybe it's just something with the code! Thank you.
 
Phys_Boi said:
The acceleration continues
... in which case the velocity keeps on changing. An orbit can be seen as an ongoing fall by missing the target. Its an equilibrium.
 
How would you calculate the changing velocity?
 
Phys_Boi said:
How would you calculate the changing velocity?
You did it by taking steps in seconds. If it's going on, another <-1,-2> will be added every second. The initial <-3,0> will have less and less influence on the overall direction.

Have a look on the Wikipedia pages here:
https://en.wikipedia.org/wiki/Centripetal_force
https://en.wikipedia.org/wiki/Centrifugal_force
https://en.wikipedia.org/wiki/Circular_motion#Uniform_circular_motion
https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

This should help your calculations.
 
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