- #1
Oliver321
- 59
- 5
Hello everyone.
Probably this question is trivial, but nevertheless I am confused about Newtons law of motion:
$$F=G\frac{m_1m_2}{r^2}$$
Now, some sources say, that F is the force between the two masses m1 and m2. Other sources say, that F is the force that m1 exhibits on m2. But isn’t this a contradiction? Because of Newtosns third law, if F is the force between the two masses, m1 acts on m2 by a a force of F/2 and vice versa.
On the other hand, if F is the force of m1 on m2, the whole force between both particles is 2F.
Also it is a bit confusing for me: I can rewrite F as
$$F=m_2a$$
if F is the force of m1 on m2.
But if F is the force between two masses rather than the force of one mass on the other, it should be stated that
$$F=\mu a$$
with μ the reduced mass. In this form it is used to solve the Kepler-problem. But on the other hand it is often stated, that the acceleration is only dependent on the mass which produces the field (the acceleration of a falling stone is independent of the mass of the stone), suggesting the first form F=m2*a.
Where is now my mistake? Or are both views compadible with each other (and why)?
I hope you understand why I am confuse and in this sense I would appreciate every help. Thanks!
Probably this question is trivial, but nevertheless I am confused about Newtons law of motion:
$$F=G\frac{m_1m_2}{r^2}$$
Now, some sources say, that F is the force between the two masses m1 and m2. Other sources say, that F is the force that m1 exhibits on m2. But isn’t this a contradiction? Because of Newtosns third law, if F is the force between the two masses, m1 acts on m2 by a a force of F/2 and vice versa.
On the other hand, if F is the force of m1 on m2, the whole force between both particles is 2F.
Also it is a bit confusing for me: I can rewrite F as
$$F=m_2a$$
if F is the force of m1 on m2.
But if F is the force between two masses rather than the force of one mass on the other, it should be stated that
$$F=\mu a$$
with μ the reduced mass. In this form it is used to solve the Kepler-problem. But on the other hand it is often stated, that the acceleration is only dependent on the mass which produces the field (the acceleration of a falling stone is independent of the mass of the stone), suggesting the first form F=m2*a.
Where is now my mistake? Or are both views compadible with each other (and why)?
I hope you understand why I am confuse and in this sense I would appreciate every help. Thanks!