Differential solar gravitational forces on the Earth-Moon system produce three effects: 1) they elongate the Moon’s orbit at quadrature (first or last quarter), 2) they cause the perigee of the Moon’s orbit to precess, and 3) they cause a torque on the inclined orbit, which causes the line of nodes to regress westward. The short summary is that as a result, the Moon’s orbit is not a simple ellipse.

A projectile is shot directly away from Earth’s surface. Neglect the rotation of Earth.What multiple of Earth’s radius RE gives the radial distance a projectile reaches if (a) its initial speed is 0.500 of the escape speed from Earth and (b) its initial kinetic energy is 0.500 of the kinetic energy required to escape Earth? (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

8-24. An Earth satellite has a perigee of 300 km and an apogee of 3,500 km above Earth's surface. How far is the satellite above Earth when (a) it has rotated 90° around Earth from perigee and (b) it has moved halfway from perigee to apogee?

(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 160 km above Earth's surface?  (b) What is the period of revolution?  Take the mass of earth as 5.98×1024 kg and the radius as 6.37×106 m

A 639-kg satellite is in a circular orbit about Earth at a height ℎ=1.09e7h=1.09e7 m above the Earth's surface. Find (a) the gravitational force acting on the satellite, (b) the satellite's speed (magnitude of its velocity, notnot  its angular velocity), and (c) the period of its revolution. Caution: The radius of the satellite's orbit is not just its height above the Earth's surface. It also includes the radius of the Earth. The mass of the Earth is 5.98×10245.98×1024 kg, and the radius of the Earth is 6.38×1066.38×106 m.

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth's rotation). Calculate the radius of such an orbit.

A satelite is in geostationary orbit. How much energy is required to move it to a circularorbit where it orbits the Earth once in 8 days? You may express your answer in terms ofthe total energy of the initial geostationary orbit.

A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17 440 km and 13 950 km, respectively. Knowing that the speed of the satellite at point C is 4.78 km/s, determine (a) the speed at point A, the perigee, (b) the speed at point B, the apogee.

A satellite moves in a circular orbit around the earth at a speed of 5000 m/s determine (a) the altitude of the satellite above the surface of Eakth (b) the period of the satellite's orbit. (c) If the mass of the satellite is doubled, will the orbital speed increase, decrease, or stay the same.

What are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4 * 105 J per orbital revolution. Adopting the reasonable approximation that the satellite’s orbit becomes a “circle of slowly diminishing radius,” determine the satellite’s (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f ) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth’s center conserved for (g) the satellite and (h) the satellite–Earth system (assuming that system is isolated)?