A 41 kg satellite is in a circular orbit around Earth with an orbital radius of 4.23 x 10^7 m. Earth's mass is 5.97 x 10^24 kg. Calculate the magnitude of the gravitational force on the satellite.

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 ?

Awheelhas a radius of 4.8 m. howfar (path length) does a point on the circumference travel if thewheel is rotated through angles of 30°, 30 rad, and 30 rev,respectively?

An object is 10 cm from the mirror, its height is 1 cm and the focal length is 5 cm. what is the image height? (indicate the object orientation by including the + or - sign with the answer.) hi = cm +1 -1 +10 -10