How can Newtonian gravity be converted to m/s without prefix?

[TheNormalForc]

Before I inundate you with various elementary problems I'm facing, I need help with the concept.

Fgrav=(GMm)/(r^2)

So Fgrav is in units of Newtons, correct? How would one convert that to m/s?

 

[kkrizka]

Gravity is just a force an object with mass experiences, which can be translated to acceleration with Newton's 2nd Law, F=ma. It has nothing to do with velocity (which has units m/s). However you can turn it into units of m/s^2, which is the units of acceleration with the above mentioned law: a=F/m, therefore:
$$a_{gravity}=\frac{GM}{r^2}$$

Where M is the mass of the object that is creating the gravitational field, not the "accelerating object".

 

[Moetasim]

Yes, Fgrav is in units of Newtons. To convert Newtons to m/s, we need to consider the equation F=ma, where F is the force in Newtons, m is the mass in kilograms, and a is the acceleration in m/s^2. We can rearrange this equation to solve for a, which gives us a=F/m. So, to convert Newtons to m/s, we need to divide the force by the mass. In the case of Newtonian gravity, the force is given by Fgrav=(GMm)/(r^2), where G is the gravitational constant, M is the mass of one object, m is the mass of another object, and r is the distance between the two objects. So to convert Fgrav to m/s, we would divide it by the mass of one of the objects involved in the gravitational interaction. However, it's important to note that this conversion only applies to the acceleration due to gravity, not the force itself.