Earth & Space Science
Gravitational force will be described as the force that controls the interaction between objects. You will use our Solar System to model different types of gravitational interactions.
After completing this tutorial, you will be able to complete the following:
Sir Isaac Newton is credited with mathematically describing how objects move through the Universe. His First law of Motion describes what Galileo called inertia, the idea that an object in motion tends to stay in motion (with a constant speed and direction) unless acted upon by an outside force. His Second Law of Motion shows a mathematical relationship between the force exerted by an object and that object's mass and acceleration (F = ma). Newton's Third Law of Motion states that for every action there is an equal and opposite reaction.
Newton went on to explain the relationship between the above described forces and gravity. His Law of Universal Gravitation shows that the force exerted between objects (F) is directly related to their combined masses (m1 and m2) and inversely proportional to the square of the distance between them (r). The force is also related to the gravitational constant, G, which has a universal value. Newton's equation for Universal Gravitation is:
When considering the relationship between objects in the Universe, the force between those objects depends on their masses and the distance between them, specifically between their center of mass.
An example of these laws working together is our Solar System. We have a massive object in the center (the Sun) surrounded by smaller objects (the planets, asteroids, moons, comets, etc). Each of the smaller objects has a mass and a velocity and, in the absence of an external force, would move in a straight line at a steady speed (Newton's First Law of Motion). However, each individual object is affected by an outside force - primarily the gravitational force of the Sun but also of the other objects in the Solar System. The result of the Sun's gravitational influence on the smaller objects is easily observed; the smaller objects orbit the Sun because of its gravitational force. This relationship between inertia and Universal Gravitation is referred to as Uniform Circular Motion. In the Law of Uniform Circular Motion, Newton states that a massive object can change the trajectory of an object near it. If the central object has enough mass compared to the other object, that changing trajectory can result in a (near) circular orbit. This force is referred to as centripetal force and it simply means the force that pulls an object towards the center of mass of another object.
Using the Earth as an example, the Sun pulls the Earth towards it due to its gravitational force. Because the Earth has its own speed, it isn't pulled into a collision. The result of this balance between gravitational force and speed is the orbit of the Earth around the Sun. It isn't a perfect circle (which is the theoretical result of Uniform Circular Motion) due to the influence of the other objects in the Solar System and the Earth's own tiny influence on the Sun.
The further an object is from the center of mass of the Sun, the weaker the gravitational force will be (distance and force are inversely related). So, the further the object is from the Sun, the less circular the object's orbit will be. Comets have very elliptical orbits because of their distance from the Sun, and their proximity to and interactions with other objects that conflict with the influence of the Sun's gravitational force.
|Approximate Time||25 Minutes|
|Pre-requisite Concepts||Students should be familiar with gravity, motion, velocity, planets in Solar System, the Moon, and comets.|
|Course||Earth & Space Science|
|Type of Tutorial||Concept Development|
|Key Vocabulary||asteroids, celestial objects, comet|