How Does Universal Gravitation Apply in Planetary Simulation Errors?

[m3the01]

Most likely a basic question to most, been awhile since I've done any of this.

If i remember right the formula states, F = G*M_1*M_2/d^2

where d = distance between M_1 and M_2

Im creating a planetary simulator for fun, i get the initial position of the Earth using the 7 variable Astrological Guides technique.

iniPos

I then get a position + 1 day in the future call it pos2;

Velocity = pos2-iniPos;
Im using the grav-constant 6.67E-20 km^3/kg*s^2

1)So grav_constant*M_1*M_2 = grav_const*5.9742E24*1.988435E35
= 7.923498687E35

2)The distance between the the two is approx 150 000 000, according to the formula then d^2 = 2.25E16

Force = grav_constant*M_1*M_2/d^2 = 3.52155E19 km*Kg/s^2

Huge number!

Forward Euler update shows us that the 'unit_vector' pointing towards the sun multiplied by the force should give us our update method.

updateVelVector = oldVelVector + unit_vector*force*dt

Where dt = change in time

However this doesn't work worth a damn,

Somewhere I've made a mistake and i just can't see it,

Please help!

PS i tried reducing the problem space to some number which i thought would be easier to use. I decided to decrease the distance to 1 km, basically this turns the problem into earth_mass/1.125E16 and sun_mass/1.125E16. This is wrong too, I am very stuck!

 

[jtbell]

updateVelVector = oldVelVector + unit_vector*force*dt

force * dt is the impulse of the force during the interval dt, which equals the change in the object's momentum (mv), not the change in velocity.

 

[m3the01]

Could u explain a little further?

I thought the update form for velocity was

vel = oldVel + unit_vec*force*dt;
pos = oldPos + vel*dt;

Hmmm, arggg.

thanks for the help,

 

[m3the01]

Sorry guys my mistake,

For my initial velocity i forgot,

V_i/(24*3600)

Seconds not days, arggggg!

thanks for the help,

Great forum!

Steven