Gravity equation question.

[Thorham]

Hi,

 

My question should be simple enough: If (G*m1*m2)/distance^2 gives you the total amount of gravitational force, then how can I calculate the acceleration for each individual mass? I'm trying to write a simple simulation program, but I can't read some of the math that I've looked up.

 

Any help is appreciated

[timo]

You'd get the acceleration from F=ma => a=F/m. But I have the feeling your problem rather is to find the gravitational force.

[Thorham]

You'd get the acceleration from F=ma => a=F/m. But I have the feeling your problem rather is to find the gravitational force.

Thanks

 

Didn't think it would be that easy, because I was reading the Wikipedia article about this equation, and I was looking at it's vector form (which I can't read completely). Anyway, getting the force seems easy enough. 

[timo]

Well, force and acceleration are vectors, I merely didn't write down the arrows over the letters. I could also write it as [math] \vec F = m\vec a \Rightarrow \vec a = \vec F / m[/math]. Like I said, I'd rather expect you to have problem finding the force, i.e. the force vector. It's not that hard, but if you get stuck, you're welcome to ask for more help here. For question about forces and working with vectors there should be plenty of people in this forum that can and will gladly help you.

[Thorham]

The only problem with the main formula is the gravitational constant:

 

 

Where I don't know how to read this part: m^3 kg^-1 s^-2 and N(m/kg)^2

 

For the rest my program simply does this:

 

xd=(x(t1)-x(t))
yd=(y(t1)-y(t))

pd1=xd*xd+yd*yd
pd=Sqr(pd1)

f=(m(t)*m(t1))/pd1
a1=f/m(t)
a2=f/m(t1)

xpd=xd/pd
ypd=yd/pd

xv(t)=xv(t)+xpd*a1
yv(t)=yv(t)+ypd*a1
xv(t1)=xv(t1)-xpd*a2
yv(t1)=yv(t1)-ypd*a2

This seems to work quite well, but may still be wrong.

[swansont]

The only problem with the main formula is the gravitational constant:

 

 

Where I don't know how to read this part: m^3 kg^-1 s^-2 and N(m/kg)^2

 

Those are the units in the SI system. Force is in Newtons (N), which is kg-m/s^2, because F=ma. m has units of kg, a has units of m/s^2

 

Negative exponents mean they are in the denominator

 

Since you have GMm/r^2, those are he units you need to make the force come out in N

[Thorham]

Those are the units in the SI system. Force is in Newtons (N), which is kg-m/s^2, because F=ma. m has units of kg, a has units of m/s^2 Negative exponents mean they are in the denominatorSince you have GMm/r^2, those are he units you need to make the force come out in N

Thanks

 

Yeah, of course, the SI units. I was reading m^3 kg^-1 s^-2 as mass^3*kilogram^-1*whatever^-2, should be length^3*mass^-1*time^-2.

[pmb]

Well, force and acceleration are vectors, I merely didn't write down the arrows over the letters.

It's easier to bold the letters. That's what I do. It's soooo much simpler for me and I'm soooo lazy. It looks more like what appears in texts too. E.g.

 

P = m₀U

 

p= mv

Edited May 18, 2012 by pmb