I'm trying to figure out how to properly calculate the gravitational force between two celestial objects:

Example

Mass01 = 5.97e24 (kg)

Mass02 = 1.99e30 (kg)

Distance = 1.50e11 (m)

Gconst = 6.67e-11

So the formula for calculating gravitational force is: F=G(M*m/d^2)

This is how I calculated:

Note: Red represents the calculation I did on that step.

F=6.67e-11(5.97e24*1.99e30/1.50e11)

(=) F=6.67e-11(11.88e54/1.50e11)

(=) F=6.67e-11(7.92e43)

(=) F=5.283e33 (rounded)

Did I calculate this improperly or am I being paranoid?

Yup, that, so it is of the order of 1022ish

You're going to get big numbers anyway, you need a big force to accelerate a big mass.

It looks like you forgot to square the distance.

*gasp* You're right! Thank you. Aside from that, does everything else look ok?

Thanks for the help everyone :D

out of operators priority, it should be F=G((M*m)/d^2)

The brackets are redundant here. By operator precedence F = G * M * m / d^2 is perfectly correct.

So the formula for calculating gravitational force is: F=G(M*m/d^2)

out of operators priority, it should be F=G((M*m)/d^2)

Newton theory is good for a capiptal absolute moment in universe, and fits well linear space, but count time in, and you will need super small timestep to update linear vectors as often as possible (still a theory, some believe in a linear time quantum). Einstein theory fits time better, yet newton is sufficient usualy with resolution of 0.1 second! But forget simulating two base balls of sun mass one meter from eachother. You cannot express such a small number to step in time to have them not on oposite side of universe, they will accelerate towards eachother toooooooo much, like speed of light * speed of light. Funny

Since my plan is to produce a simulation, could you give me some pointers as to where I should look for further information on what you just explained.

P.S. I'm usually not a nitpicker, but, for future reference, try to be more careful with the way you structure your sentences because I had a hard time understanding what you were trying to say. Having said that, I don't know if english is your first language and I apologize if I offend you with this; it is not my intention.