Question

Write an expression to state the laws of universal gravitation in vector form.

Answer 1

Hey Mate..

Newton’s law of gravitational attraction between two masses states that, the gravitational force is directly proportional to the individual masses and inversely proportional to the square of the distance between the two and acts along the line joining them.

To represent the law in terms of vectors,

Let m1 and m2 be point masses at positions r1→ and r2→.

If

r12 → = r1 → − r2 → here r12→ points from m2 to m1 and r12^ is a unit vector in the direction of r12 →  and r12=∥r1 → − r2 → ∥ is the simple distance between the two massess

similarly

r21 → = r2 → −r1 →  here r21 → points from m1 to m2 and r21^ is a unit vector in the direction of r21 →  and r21 = ∥r2 → − r1 → ∥ is again the simple distance between the two masses

The force of gravitation on each mass is:

Fgm1→=−Gm1m2r122r12^

Fgm2→=−Gm1m2r212r21^

where G is the universal gravitational constant.

Thank You...

Answer 2

Heya...

This is the equation I'm having trouble with:

GMmr2=md2rdt2

That's the non-vector form of the universal law of gravitation on the left and Newton's second law of motion on the right. I assume that upon correctly modeling and solving this, I will have a function of time that gives the distance from a spherical mass in space (e.g. distance from the Earth from an initial condition of

r(0)=10,000km

r(0)=10,000km

Thank you