Fast transfer assuming earth and mars are starting with an angle of separation (a) of 41.24°, calculate the following for a 150 day fast transfer to mars (assume the voo vector is aligned with the earth velocity vector-earth is the periapsis of the transfer orbit): (a) the final position of mars (a ) in its orbit (at interception) relative to earth's initial position (at launch) (degrees) (b) the semimajor axis (a) and eccentricity (e) for the transfer orbit. (c) the launch vehicle c3 required to launch into the transfer orbit (km²/s? ) (d) the spacecraft delta-v magnitude required to enter martian orbit (km/s)

Which of the following is the phase that results when the moon is on the opposite side of the earth from the sun? a. quarter moon b. crescent moon c. new moon d. full moon

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r

How does the electric potential energy between two charged particles change if one particle is reduced by a factor of 3? a. increased by a factor of 3 b. it is decreased by a factor of 9 c. it is reduced by a factor of 3 d. it is increased by a factor of 9