4. Show that when a satellite is in elliptical orbit, its speed v is given by 2 v² = k = k (²=- - ² ) and when in parabola orbit v² = 2k r

13–126. The rocket is traveling around the earth in free flight along the elliptical orbit. If the rocket has the orbit shown, determine the speed of the rocket when it is at A and at B. A - 30 Mm - 20 Mm -

A satellite of mass  243kg orbits the Earth at a constant speed in a circular orbit. The work done by the Earth on the satellite is a. negative. b. zero. c.directed towards the centre of the orbit. d. [None of the others.] e. positive. f.directed along a tangent to the orbit.

3. You are a person with incredible arm strength. You throw a ball of mass m = 2 kg horizontally with initialy velocity vo. (a) How quickly would you have to throw the ball so that the ball enters a perfectly circular orbit around Earth? (Assume your height is much less than Earth's radius). (b) How long would the ball take to complete one orbit? (c) Let's say you throw the ball with 1.2x the speed found in (a). What is the semi-major axis of the new elliptical orbit of the ball? (d) How long would it take for the ball to complete its new orbital jour- ney?

(a) A planet is in an elliptical orbit around a distant star. At its closest approach, the planet is 0.580 AU from the star and has a speed of 54.0 km/s. When the planet is at its farthest distance from the star of 37.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 x 10¹¹ m. You may assume that other planets and smaller objects in the star system exert negligible forces on the planet.) km/s (b) What If? A comet is in a highly elliptical orbit around the same star. The comet's greatest distance from the star is 20,900 times larger than its closest distance to the star. The comet's speed at its greatest distance is 2.70 x 10-² km/s. What is the speed (in km/s) of the comet at its closest approach? km/s

29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of energy and angular momentum.

Copied! Problems us rce *24 Compute the orbital radius of an earth satellite that has an equatorial orbit and always remains above a fixed point P on the earth's surface. Communication satel- lites have such "geosynchronous" orbits (Fig. 6-19). These satellites are used to relay radio and television signals around the world. s if un- hate Communication satellite wwwwwwww as a dius mmm Fig. 6-19 25 The earth orbits the sun in an approximately circular orbit of radius 1.496 X 10" m (about 93 million 15

A 1000 kg object is found heading towards the Earth. At the moment it is 4 Earth radii away from the surface of our planet the asteroid is moving at 100 m/s. If it collides with our planet, how fast will it be moving right before it hits the surface? How much kinetic energy is going to be released in this collision?

4. To calculate the energy necessary to move from one situation to another we compare the total energy in each. How much work must be done by a rocket engine to transfer a 1000 kg satellite from an orbit of radius 2R, to 3R,?

SSM (a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?