Force components between two bodies

[doymand]

I am making an n-body simulator, but I'm stuck. How can I find the components of the Force acting between two bodies such as the Earth and the Sun. I know it's-

F * Cos(theta) and F * Sin(theta) but if I don't know the angle how can I find the components?

I'm using the diagram on this website but I'm still baffled.
http://www.cs.princeton.edu/courses/archive/spr01/cs126/assignments/nbody.html

 

[Simon Bridge]

if I don't know the angle how can I find the components?

You can't.

If you can encode the locations of each body, then you know the angle.
Exploit your coordinate system.

 

[nhmllr]

I don't know what language you're using, but a lot of them have an easy,built in method of putting two points into a method/function, and getting out the angle between them. Things like Java should have a class for that, it might me contained in the regular "Math" class but I'm not sure.

You could also find the sines and cosines of the angles YOURSELF with your coordinates easily. Find the distance between your two points using the pythagorean theorem/distance formula, call it d
Say the difference in height is h, and the difference in width is w
(d² = h²+w²)

sinθ = h/d
cosθ = w/d

 

[doymand]

Thanks, in my search for a complex answer I forgot that I knew the positions of both of them and could easily find the angle.

 

[pmacias]

I understand your confusion and I am happy to help you find a solution to your problem. The components of force between two bodies can be calculated using the vector components of the force and the angle between the two bodies. In this case, the force is the gravitational force between the Earth and the Sun, which can be calculated using Newton's law of gravitation (F = G * m1 * m2 / r^2).

To find the components of this force, you will need to use trigonometric functions. The force vector can be broken down into its horizontal and vertical components using the angle between the two bodies (theta) as follows:

Fx = F * cos(theta)
Fy = F * sin(theta)

If you do not have the angle between the two bodies, you can use the inverse trigonometric functions (cos^-1 and sin^-1) to calculate it. For example, if you know the x and y components of the force and want to find the angle, you can use:

theta = cos^-1 (Fx / F)
or
theta = sin^-1 (Fy / F)

Alternatively, you can also use the Pythagorean theorem to find the magnitude of the force (F) and then use the above equations to find the components.

I would also recommend checking the units of your calculations to ensure they are consistent. The gravitational constant (G) has units of m^3/kg*s^2, so make sure to convert your masses and distances to the appropriate units.

I hope this helps you in your n-body simulator and please let me know if you have any further questions. Good luck!