How to Derive Velocity Components in a Gravitational Orbit Simulation?

[FLOUR]

Hello,
considering a Planet 1 and a Planet 2, where 1 is extremely heavier than 2 and 2 is going in Planet 1's orbit. Two questions

1) howto get the expression v = - G m2 m1 / r

2) if we consider the energy < 0, we can get to an expression as
v < sqrt (2GM2 / r)

howto get Vx and Vy for that V ?

(r is the radius.)

Hints and other help are welcome. Thanks.

 

[pervect]

Hello,
considering a Planet 1 and a Planet 2, where 1 is extremely heavier than 2 and 2 is going in Planet 1's orbit. Two questions

1) howto get the expression v = - G m2 m1 / r

The 'v' in this expression is potential energy. It's just the intergal of F= Gm1m2 / r^2.

Some of your other 'v's look like they might be velocity.

 

[FLOUR]

The 'v' in this expression is potential energy. It's just the intergal of F= Gm1m2 / r^2.

Some of your other 'v's look like they might be velocity.

Oh... that's why couldn't get a Velocity experssion like that.

The second is for velocity, taken from the mecanical energy expression and using e<0. So since velocity is a vector, v = vx + vy and we have an expression for the scalar value of v, how can we get each of the components? This is necessary for setting up the initial values in a simulation program.

Thanks.