Final answer:
The gravitational potential energy of a spacecraft at escape velocity is sufficiently overcome by its kinetic energy, resulting in a total mechanical energy of zero or greater. Thus, at escape velocity, an object becomes unbounded from the celestial body's gravity. The ratio of kinetic to potential energy decreases for larger orbits, and several true/false statements regarding gravitational concepts are elaborated upon.
Step-by-step explanation:
The question concerns the gravitational potential energy and kinetic energy of a spacecraft when it reaches the escape velocity. In physics, escape velocity is defined as the minimum velocity an object must have to break free from a celestial body's gravitational attraction without further propulsion. We know that gravitational potential energy (GPE) is negative because an arbitrary zero level is commonly chosen at infinite distance where the potential energy is thus zero. An object has to overcome this negative potential well with sufficient kinetic energy to escape the gravitational pull.
When an object reaches escape velocity, its total mechanical energy (the sum of its kinetic energy and its gravitational potential energy) is zero or greater. The kinetic energy required for escape depends on the mass of the planet and the distance from the center of mass where escape is attempted. To escape, all of the gravitational potential energy, which can be calculated with the formula GPE = -G(Mm)/r where G is the gravitational constant, M is the mass of the celestial body, m is the mass of the object, and r is the distance from the center of mass, must be overcome or matched by the object's kinetic energy.
The question 'is there a trend to the ratio of kinetic energy to change in potential energy as the size of the orbit increases?' points out that for larger orbits, this ratio decreases since the change in potential energy diminishes more slowly with distance than the square of the velocity (which determines kinetic energy). The answer to question 8 is False: throwing a rock into the air increases its gravitational potential energy, not kinetic, and as it falls back down, the potential energy converts back into kinetic energy, increasing its velocity.
As for the true/false statements, the answer to number 29 is True, a spacecraft will travel in a straight line until acted upon by another force. The answer to number 24 about a solar sail craft is True; it is possible to propel it using particles from the solar wind. Number 38 is True, since the formula for gravitational potential energy (U = mgh) shows that joules (J) are equivalent to the product of mass, gravitational acceleration, and height squared, which is kg×m×(m/s)². Number 46 is also True; an external force is necessary to move a stationary object in space. Lastly, question 3 is True, describing the need for an isolated planet-satellite system to follow Kepler's laws.