Unit 7 Overview: Gravitation

Introduction

Gravitation is one of the fundamental forces of nature, and it governs the behavior of objects on a cosmic scale. The force of gravity is what keeps planets in orbit around stars and moons in orbit around planets. In this article, we will explore the basics of gravitational forces and how they relate to the orbits of planets and satellites.

Key Vocabulary

• • Gravity - The force of attraction between two objects with mass.
• • Orbit - The path of an object as it revolves around another object in space.
• • Elliptical orbit - An orbit that is shaped like an ellipse, which is an elongated circle.
• • Orbital velocity - The speed at which an object must travel to maintain a stable orbit around another object.
• • Mass - The amount of matter in an object.
• • Distance - The amount of space between two objects.
• • Escape velocity - The minimum speed an object needs to escape the gravitational pull of a planet or other celestial body.
• • Period - The time it takes for an object to complete one orbit around another object.
• • Solar system - The collection of planets, moons, and other celestial objects that orbit around the Sun.

Key Questions

• • What is gravitation?
• • What is gravity and how is it related to mass?
• • What is an orbit and how does it work?
• • What is the difference between a circular orbit and an elliptical orbit?
• • What is the relationship between distance and gravitational force?
• • What is orbital velocity and how is it related to an object's mass and distance from the object it is orbiting?
• • What is escape velocity and how does it relate to gravitational force?
• • What is the period of an object's orbit and how is it related to its distance from the object it is orbiting?
• • How does the gravitational force between two objects change as their distance from each other changes?
• • What is the solar system and how do the planets and other celestial objects interact with each other through gravitation?

7.1 Gravitational Forces

Gravitational forces are the forces of attraction between any two objects in the universe. 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 them. In other words, the greater the mass of the two objects and the closer they are to each other, the stronger the gravitational force between them.

One of the most famous examples of gravitational forces is the force of Earth's gravity on objects near its surface. This force is what keeps us and all other objects on the surface of the Earth. The force of gravity also keeps the Moon in orbit around the Earth, and the Earth in orbit around the Sun.

The force of gravity is not only responsible for keeping planets in orbit around stars, but it also plays a crucial role in the formation of stars and planets themselves. Gravity is what causes clouds of gas and dust in space to collapse and form stars, and it is also what causes planets to form around those stars.

7.2 Orbits of Planets and Satellites

The orbits of planets and satellites are the result of the gravitational forces acting upon them. In general, objects in orbit are constantly falling towards the object they are orbiting, but they are also moving forward fast enough that they miss the object and continue to orbit around it. This is known as an elliptical orbit. 

The shape of an orbit depends on the strength of the gravitational force between the two objects and the initial velocity of the orbiting object. If the velocity is too low, the object will fall towards the object it is orbiting and crash into it. If the velocity is too high, the object will escape the gravitational pull and move away from the object it is orbiting.

The speed at which an object must travel to maintain a stable orbit around another object is known as the orbital velocity. The orbital velocity depends on the mass of the object being orbited and the distance between the two objects. For example, the Moon orbits the Earth at a distance of about 238,855 miles, and its orbital velocity is approximately 1.022 kilometers per second.

Practice Problems

• • __What is the gravitational force between two objects with masses of 100 kg and 500 kg that are 10 meters apart?__Answer: F = G x (m1 x m2) / r^2 = (6.67 x 10^-11 N m^2 / kg^2) x (100 kg x 500 kg) / (10 m)^2 = 3.335 x 10^-7 N
• • __What is the orbital velocity of a satellite orbiting Earth at a distance of 500 km?__Answer: v = sqrt(G x M / r) = sqrt((6.67 x 10^-11 N m^2 / kg^2) x (5.97 x 10^24 kg) / (500 km + 6,371 km)) = 7,664 m/s
• • __What is the escape velocity of an object on the surface of Earth?__Answer: ve = sqrt(2GM/r) = sqrt(2 x (6.67 x 10^-11 N m^2 / kg^2) x (5.97 x 10^24 kg) / 6,371 km) = 11.2 km/s
• • __What is the period of a satellite in a circular orbit around Earth at an altitude of 500 km?__Answer: T = 2 x pi x sqrt(r^3 / GM) = 2 x pi x sqrt((500 km + 6,371 km)^3 / (6.67 x 10^-11 N m^2 / kg^2) x (5.97 x 10^24 kg)) = 5,647 seconds or approximately 94 minutes
• • __What is the gravitational force between the Sun and Earth?__Answer: F = G x (m1 x m2) / r^2 = (6.67 x 10^-11 N m^2 / kg^2) x (5.97 x 10^24 kg x 1.99 x 10^30 kg) / (149.6 x 10^6 km)^2 = 3.52 x 10^22 N

Conclusion

In conclusion, gravitational forces play a critical role in the behavior of objects in space, from the formation of stars and planets to the orbits of planets and satellites. Understanding the basic principles of gravitational forces is essential for understanding the universe and our place within it.