The following equation, derived from Newton's version of Kepler's third law, allows us to calculate the mass (MMM) of a central object, in solar masses, from an orbiting object's period (ppp) in years and semimajor axis (aaa) in astronomical units: M=a3p2M=a3p2 Using this formula with the values you found in Parts C and D, what is the approximate mass of the central object?

In positive numbers less than 1, the zeros between the decimal point and a non-zero number are blank significant

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

Athin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. a) what is the magnitude of the electric field due to the rod at z = 0? n/c (b) what is the magnitude of the electric field due to the rod at z = infinity? n/c (c) in terms of r, at what positive value of z is that magnitude maximum? r (d) if r = 4.00 cm and q = 9.00 µc, what is the maximum magnitude? n/c