On a cosmic calendar, in which the history of the universe is compressed into one year, when did kepler and galileo first discover that we live on a planet in a solar system

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Aplane flies directly between two cities, a and b, which are separated by . from a to b, the plane flies into a headwind. on the return trip from b to a, the wind velocity is unchanged. the trip from b to a takes less than the trip from a to b. what is the airspeed of the plane, assuming it is the same in both directions

Me with this and you will be marked brainliest