Gravitational Path of an Object

  • #1
461
0

Main Question or Discussion Point

What is the path of an object entering the graviational pull starting at a point [tex][x_{0}, y_{0}, z_{0}][/tex] with a velocity [tex][V_{0x}, V_{0y}, V_{0z}][/tex] neglecting air resistance? This is what I have thus far:

[tex]x(t)=x_{0}+V_{0x}*t-g_{x}*t^{2}[/tex]
[tex]y(t)=y_{0}+V_{0y}*t-g_{y}*t^{2}[/tex]
[tex]z(t)=z_{0}+V_{0z}*t-g_{z}*t^{2}[/tex]

where
[tex]g_{x}=\frac{G*M}{r_{x}}[/tex]
[tex]g_{y}=\frac{G*M}{r_{y}}[/tex]
[tex]g_{z}=\frac{G*M}{r_{z}}[/tex]

and the axis projected on the r-axis
[tex]r_{x}=x*cos\theta*sin\phi[/tex]
[tex]r_{y}=y*sin\theta*sin\phi[/tex]
[tex]r_{z}=z*cos\phi[/tex]

After introducing [tex]\theta[/tex] and [tex]\phi[/tex] the whole thing becomes difficult. Is there an easier way?
 

Answers and Replies

  • #2
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
682
What is the path of an object entering the graviational pull starting at a point [tex][x_{0}, y_{0}, z_{0}][/tex] with a velocity [tex][V_{0x}, V_{0y}, V_{0z}][/tex] neglecting air resistance? This is what I have thus far:

[tex]x(t)=x_{0}+V_{0x}*t-g_{x}*t^{2}[/tex]
[tex]y(t)=y_{0}+V_{0y}*t-g_{y}*t^{2}[/tex]
[tex]z(t)=z_{0}+V_{0z}*t-g_{z}*t^{2}[/tex]

where
[tex]g_{x}=\frac{G*M}{r_{x}}[/tex]
[tex]g_{y}=\frac{G*M}{r_{y}}[/tex]
[tex]g_{z}=\frac{G*M}{r_{z}}[/tex]
NO!

Philosophaie, based on your other posts, you have a marked tendency to apply equations randomly and incorrectly. Correcting these equations would be a disservice to you because you not understand the theory. Without this understanding, you might use the right equation this time, but you will use the wrong equations again in the future. Please, read a book. Here are three:

Bate, Mueller, White, "Fundamentals of Astrodynamics". [URL]https://www.amazon.com/dp/0486600610/?tag=pfamazon01-20[/URL][/URL]
Cost at Amazon: $16.61

Vallado, "Fundamentals of Astrodynamics and Applications". [URL]https://www.amazon.com/dp/1881883140/?tag=pfamazon01-20[/URL]
Cost at Amazon: $63.95.

Roy, "Orbital Motion". [URL]https://www.amazon.com/dp/0852742290/?tag=pfamazon01-20[/URL]
Cost at Amazon: $70.00.

Cost of these at a library: Free.
 
Last edited by a moderator:

Related Threads for: Gravitational Path of an Object

Replies
10
Views
1K
Replies
1
Views
2K
Replies
5
Views
493
  • Last Post
Replies
2
Views
1K
Replies
7
Views
461
Replies
2
Views
4K
  • Last Post
Replies
4
Views
726
Replies
4
Views
2K
Top