norm[xx:{__}]:=(Sqrt[xx.xx])
norm[{x,y,z}]
norm[xx:{__}]:=(Sqrt[Plus@@(xx^2)])
norm[{x,y,z}]
norm[xx:{__}]:=(Sqrt[Plus@@(#^2&/@xx)])
norm[{x,y,z}]

AstronomicalData["Earth","Mass"]

AstronomicalData["Earth","Position"][[{1,2}]]

AstronomicalData["Earth","Position"]

ClearAll[berdva]
vect={12,45,65}
berdva[v_List]:=Drop[v,-1]
berdva[vect]

ClearAll[a]

a="neco"

vect/.{a_,b_,c_}->{a,b}

vect/.{a_,b_,c_}:>{a,b}

vcemmazu={1,1.,x,(c^b)};
DeleteCases[vcemmazu,((_)^(_))]
Select[vcemmazu,!MatchQ[#,((_)^(_))]&]

Cases[vcemmazu,Except[((_)^(_))]]

MatchQ

casTed=AbsoluteTime[]

polohaZeme[t_]:=AstronomicalData["Earth",{"Position",DateList[t]}]

posiceZemeTed=polohaZeme[casTed]

rychlostZemeTed=(polohaZeme[casTed+100]-polohaZeme[casTed-100])/200

Norm[rychlostZemeTed]

<<PhysicalConstants`

zemeParam={mZem->AstronomicalData["Earth","Mass"],r0->posiceZemeTed[[1;;2]],v0->rychlostZemeTed[[1;;2]]};

slunceParam={mSlunce->AstronomicalData["Sun","Mass"]};

globalParam={κ->GravitationalConstant[[1]]}

dosazeniAll=Union[zemeParam,slunceParam,globalParam]

rovVect={κ*mSlunce*mZem*((-r[t])/(Norm[r[t]]^3))==mZem*r''[t]}

rovDosaz=rovVect/.dosazeniAll

pocVect={r[0]==r0,r'[0]==v0}

pocDosaz=pocVect/.dosazeniAll

{rovDosaz,pocDosaz}

tmax=5*π*(10^7);
reseni=NDSolve[{rovDosaz,pocDosaz},r,{t,0,tmax}][[1]]

ParametricPlot[r[t]/.reseni,{t,0,tmax},AspectRatio->1]

Podprikladek

pomrce=r''[t]==-0.1r[t];
poc=r[0]=={1,2,3};
tmax=10;
res=NDSolve[{pomrce,poc,r'[0]=={1,2,3}},r,{t,0,tmax}]
r[0.2]/.res