Keplers law of planetary motion
1st:law of ellipses=the orbit of planets is ellipses
2nd:law of equal areas=planet don’t move with constant speed around their orbits
3rd:law of periods= T ²/R ³ is the average distance from the sun is the same for all planets
Centripetal force
A force pulls objects towards the center
On PM horizontal distance
Δx=Voxt
On PM final horizontal velocity
Vx=Vox
On PM Final vertical velocity
Vy =Voy +gt
I’m n pm vertical displacement
Δy=1/2gt ²
On pm initial velocity
Vy=gt
Time
√2 Δy/g
Range
Vox √2 Δy/g
On IM
Vox=vocos θ
Voy=vosin θ
On I’m Horizontal velocity
Vx=vocos θ
On im vertical velocity
Vy=vosin θ +gt
Displacement
Δx=Vocos θt
Δy=vosin θ+1/2gt ²
Maximum height
Vo ²sin ² θ
=Rtan θ/4
Time on im
t= vosin θ/g
Ttot
2vosin θ/g
Range on IM
Vo ²sin2 θ/g
Wav
Δ θ/t Δ
Wav
Wav
=wo+wf/2
Δ θ
Δ θ =woΔt+ 1/2α Δt²
Δ θ
Δ θ={wo+wf}/2 Δt
α
Δ w/Δt