- #1

LCSphysicist

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- Homework Statement:
- Two particles of mass m1 and m2 are released in rest, they are separated by a distance ro, and all motion is by the mutual gravitational attraction. Calc their velocity when their distance is r < ro.

- Relevant Equations:
- All below.

This problem is very easy to solve considering that the two particles belong a closed system under action of conservatives force.

My doubt is if it is possible to solve the problem by consider one particle by time, that is:

Suppose that we know the particle m one is under gravitational force, at first its energy is = -Gm1m2/ro

After certain time, the distance to the central force will be r, and so -Gm1m2/r + m1v²/2.

If we apply E1=E2, it will be wrong! The question is why, since all forces are conservative.

For example, we can say that m2 is like the earth, when we apply to m1 E1=E2 is right, but in this case no.

This make me wonder that E1 = E2 under the gravitational field of the Earth is actually a approximation (yes, good).

My doubt is if it is possible to solve the problem by consider one particle by time, that is:

Suppose that we know the particle m one is under gravitational force, at first its energy is = -Gm1m2/ro

After certain time, the distance to the central force will be r, and so -Gm1m2/r + m1v²/2.

If we apply E1=E2, it will be wrong! The question is why, since all forces are conservative.

For example, we can say that m2 is like the earth, when we apply to m1 E1=E2 is right, but in this case no.

This make me wonder that E1 = E2 under the gravitational field of the Earth is actually a approximation (yes, good).