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i need help finding the initial acceleration vector of two particles?
i'm given the masses of two particles as well as the initial position vectors for the particles, the two objects exert gravitational forces on each other. How would i find the initial acceleration vectors of the two particles? I'm just asking for equations not to have the problem solved.
1 Answer
- husoskiLv 71 decade agoFavorite Answer
Use two Newton results.
Universal gravitation gives you |F| = G*m1*m2/r², where r = |r1 - r2| is the distance between the point vectors r1 and r2 for particles of mass m1 and m2, respectively. This gives the magnitude of the force on each particle..
The 2nd law of motion gives F = ma; or a = F/m. This applies to each mass.
For direction, I'd use the unit vector u = (r2 - r1) / |r2 - r1| to represent a unit displacement in the direction from r1 to r2. Then:
F1 = |F| * u = (G*m1*m2 / r²) * u
F2 = |F| * -u = (G*m1*m2 / r²) * -u
...as the vector forces on m1 and m2, respectively. Vector acceleration follows from Netwon's 2nd, in vector form.
|a1| = |F1| / m1 = G*m2/r²
|a2| = |F2| / m2
