# Planetary Orbits

Planetary orbits are the paths that objects in space follow as they move around a star. These paths are determined by gravity, which pulls the objects towards the star. To understand how this works, we need to remember a few things about motion and gravity. Astrophysics is the study of these movements and how they shape our universe. If you're interested in learning more about planetary orbits, keep reading!

## What is the mathematical description of orbits?

Let's talk about Newton's laws! The first law we'll discuss is the law of gravitation, which explains the force of gravity between two objects with mass. It's measured by the distance between the objects and the gravitational constant, which is around 6.67 ⋅ 10-11m3/kg⋅s2. Newton's second law of motion is all about circular motion, which is when an object moves around a fixed point due to a force pulling it towards that point. We use an equation to calculate the acceleration of circular motion, which is based on the object's velocity and the radius of the circular path. When it comes to astronomical settings, we often see circular motion happening between two masses due to the force of gravity. This circular motion is maintained because the attractive force is constantly changing the direction of the orbiting body but not its speed. This means that the radius of the circle is constant, and objects in the same orbit have the same speed. To determine the orbit of a body, we need to consider both gravitational potential energy and kinetic energy.

## What types of orbits are there?

Let’s explore other possibilities of orbits that occur in our world and how they deviate from the ideal description we explored above.

**Mathematical implications of Newton’s potential energy**

Newton's potential energy can give us three types of orbits, depending on the total energy of the object. If the object has an excessively high speed compared to its radial distance, it will have a positive total energy. This means that the object will not be bound to the star and will continue moving away from it. The total energy of the object is the sum of its gravitational potential energy and kinetic energy. The equation for total energy is U + Ek. The gravitational potential energy is often represented by U or U_g.

**Types of orbits**

Newton's law of gravitation can generate three types of orbits: hyperbolic, parabolic, and elliptical. A hyperbolic orbit occurs when the total energy of a body is positive, causing it to escape the gravitational pull and move towards regions of weaker gravity. A parabolic orbit occurs when the total energy is exactly zero, causing the body to escape the gravitational pull with zero speed. An elliptical orbit occurs when the total energy is negative, causing the body to orbit the source of gravitational interaction without escaping. Ellipses have two points that determine their shape, with circles being a special case of an ellipse. Even though circular orbits are a special case, many aspects studied in circular orbits, such as the dependence of speed on radial distance, still apply to

## Examples of planetary orbits and satellite orbits

Elliptical orbits are common in our solar system, with planets orbiting the sun and moons orbiting planets. While the planets in our solar system have almost circular orbits, they still follow an elliptical path. The Earth reaches its farthest point from the sun in July and its closest point in January. Some objects, like Comet Halley, have extreme elliptical orbits and are only visible from Earth every 76 years.

Most planetary satellite orbits can be considered circular due to their initial conditions being close to those that yield circular orbits. In our solar system, Mercury and Venus have no satellites, Earth has one (the Moon), Mars has two, Jupiter has 79, Saturn has 82, Uranus has 27, and Neptune has 14.

## Planetary Orbits - Key takeaways

In astrophysics, orbits are the movements that objects make due to gravitational attraction. For certain initial conditions with negative total energy, Newton's law of gravitation causes a circular motion. However, in a more general setting, the total energy of a body can result in ellipses (including circles as a special case), parabolas, and hyperbolas as possible types of orbits. Planetary orbits and planetary satellite orbits are examples of parabola and hyperbola orbits in special settings. These orbits are almost always closed ellipses, which can be approximated by circular orbits.

## Planetary Orbits

**How many satellites does each planet have?**

Mercury and Venus have none (they are too close to the Sun and it probably attracted them), Earth has one (the moon), Mars has two, Jupiter has 79, Saturn has 82, Uranus has 27, and Neptune has 14.

**What are the orbits of the planets?**

Orbits of planets are the movement described by planets due to the gravitational attraction of other bodies, usually stars.

**What are the three orbits?**

The three types of orbits generated by Newton’s law of gravitational attraction are hyperbolic orbits, parabolic orbits, and elliptical orbits.

**What are the four types of orbits?**

There are hyperbolic orbits, parabolic orbits, elliptical orbits, and circular orbits as a particular case of elliptical.