Chapter 8, Problem 8.33P

Consider a spherical planet of mass M and radius R. How much energy is required to take a rocket of mass m from rest on the surface of the planet to a circular orbit a height h above the surface? (You may not assume h is small).

Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite? Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?

use mathematica to find the maximum distance xmax with those given valus.  SPEED M DONE WITH IT

Consider a pulsar, a collapsed star of extremely high density, with a mass M equal to that of the Sun (1.98 * 10^30 kg), a radius R of only 12 km, and a rotational period T of 0.041 s. By what percentage does the free-fall acceleration g differ from the gravitational acceleration ag at the equator of this spherical star?

Rank the magnitudes of ∮ B→ ⋅ d s→ for the closed paths a through d as shown from greatest to least.

A tunnel is dug through the center of a perfectly spherical and airless planet of radius R. Using the expression for g derived in Gravitation Near Earth’s Surface for a uniform density, show that a particle of mass m dropped in the tunnel will execute simple harmonic motion. Deduce the period of oscillation of m and show that it has the same period as an orbit at the surface.

If Force B on the x-z plane is equal to 300N and h = 4m and v = 10m, then what is the i and k components of Force B?

Calculate the interval ∆s^2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0,t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S.

Is the Schrödinger equation for a particle on an elliptical ring of semi-major axes a and b separable?