- #1
Acronim
- 6
- 0
Hi,
I wanted to find some formulas for describing the motion of two particles.
It seems, though, that it's harder than I originally thought.
The situation:
there are two particles (m1 and m2), and they are in rest somehow. Due to their mass, each particle attracts the other with a gravitational force [tex]F_g = \frac{G m_1 m_2}{d^2}[/tex], where G is the gravitational constant, d is the distance between the particles, and m1 and m2 are the masses of the particles.
Combining this with: [tex]F=m \cdot a[/tex]
Gives me: [tex]a_1 = \frac{G m_2}{d^2}[/tex]
This is already useful, of course, but I'd rather have a formula that depends on time instead of the distance between the particles.
So what I'd like to know: is there a formula for a(t)? (and/or v(t))
I guess the formula would need to exist of at least G, the initial distance between the particles and their mass, but I really don't know how it would look like.
I know that a(t) is not linear, and neither is v(t).
Also, I know that acceleration is the integral of velocity with respect to time, but since I have no t in the formula for acceleration, I have no idea how to do this integral.
(The motion of the particles is one-dimensional; they don't rotate around each other, they just move towards each other due to the gravitational forces they apply on each other.)
I hope someone can help me out![Big Grin :biggrin: :biggrin:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
I wanted to find some formulas for describing the motion of two particles.
It seems, though, that it's harder than I originally thought.
The situation:
there are two particles (m1 and m2), and they are in rest somehow. Due to their mass, each particle attracts the other with a gravitational force [tex]F_g = \frac{G m_1 m_2}{d^2}[/tex], where G is the gravitational constant, d is the distance between the particles, and m1 and m2 are the masses of the particles.
Combining this with: [tex]F=m \cdot a[/tex]
Gives me: [tex]a_1 = \frac{G m_2}{d^2}[/tex]
This is already useful, of course, but I'd rather have a formula that depends on time instead of the distance between the particles.
So what I'd like to know: is there a formula for a(t)? (and/or v(t))
I guess the formula would need to exist of at least G, the initial distance between the particles and their mass, but I really don't know how it would look like.
I know that a(t) is not linear, and neither is v(t).
Also, I know that acceleration is the integral of velocity with respect to time, but since I have no t in the formula for acceleration, I have no idea how to do this integral.
(The motion of the particles is one-dimensional; they don't rotate around each other, they just move towards each other due to the gravitational forces they apply on each other.)
I hope someone can help me out