The correct graph representing the relationship between orbital distance and the acceleration of gravity will depict the force of gravity decreasing rapidly with an increase in distance from the planet, following an inverse square law.
The question involves identifying the correct graph that shows how orbital distance relates to the acceleration of gravity on a new planet. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This implies that as the distance increases, the force of gravity (and thus the acceleration of gravity) decreases at a rate proportional to the inverse square of the distance. Therefore, the graph that correctly represents this relationship would show a curve where the force of gravity decreases rapidly as distance from the planet increases, reflecting an inverse square relationship.
Relevant Concepts for Understanding Gravitational Force and Orbits
- Newton's law of universal gravitation which describes the gravitational force between two masses.
- The fact that gravitational force (and consequently acceleration due to gravity) decreases with the square of the distance from the mass causing the gravity.
- Kepler's laws and the behavior of satellites in orbit, especially regarding the points of fastest and slowest speed within an elliptical orbit governed by the conservation of angular momentum.
Given this information, the correct graph would depict a decreasing curve that flattens out as the distance on the x-axis increases, capturing the inverse square law of gravity.