Orbital Radius and Astronomical Unit

Orbital Radius

Introduction:

Our planet Earth is a part of the solar system, which has 8 planets in total revolving around a star named the Sun. All the planets of the solar system have different compositions and are made up of different components. They are also located at different distances from the Sun, which makes them have different features such as temperature, pressure, texture, surface, and composition. In this session, we are going to look at the orbital radii of all the planets in the solar system.

Explanation:

The solar system has planets and dwarf planets and their moons, a star named the Sun, and the objects such as asteroids, meteoroids, and comets. The planets, dwarf planets, asteroids, meteoroids, and comets move around the Sun in closed paths called the ORBITS. Planets can be seen at night because they reflect light from the Sun.

The stars that we see at night all over the sky are far outside our solar system. All the orbits taken by various objects to move around the Sun are elliptical in shape. For some bodies, it is less elliptical, i.e., close to being circular. For some other bodies, it is more elliptical.

Definition of Orbital Radius:

The elliptical orbits of the planets and other bodies of the solar system around the Sun are placed such that the Sun does not lie at the center of the ellipse. In fact, it lies on one of the foci of the elliptical orbit.

Thus, the distance of a planet from the Sun is not the same at all times. This distance keeps oscillating between a maximum and a minimum value throughout the revolution of that planet around the Sun.

Perihelion is the closest point of a planet to the Sun.

For the Earth, it occurs around January 3^rd every year.

Aphelion is the furthest point of a planet to the Sun.

For the Earth, it occurs around July 4^th every year.

Astronomical Unit:

We measure the distances on Earth in the units of meters and kilometers. However, because the distance between the planets and the Sun is very large. Hence, a different unit called the Astronomical Unit is used for this purpose. The average distance between the Earth and the Sun is called 1 Astronomical Unit. It is a unit of distance used to measure the distance between planets and the Sun in the solar system.

1 AU = 1.496 x 10¹¹ m

Mathematics of Orbital Radius:

Parts of an Elliptical Orbit:

An ellipse has three measures, namely,

1. Length of the major axis, 2a
2. Length of the minor axis, 2b
3. Distance between the center of the ellipse and the focus, c

The eccentricity (e) of an ellipse is a measure of the closeness of its shape to a circle.

It is given mathematically by e =.

The eccentricity of a circle is zero.

The furthest distance between the Sun and a planet is given by (a + c).

The closest distance between the Sun and a planet is given by (a – c).

The average distance between the Sun and a planet is thus given by,

Orbital radius = a

The orbital radius of a planet is equal to the length of its semimajor axis.

Questions and Answers:

The distance between the Sun and the center of Mercury’s orbit is 1.19 x 10¹⁰ m and the length of its semi major axis is 5.79 x 10¹⁰ m. Find the eccentricity of its orbit.

Answer:

Given that,

c = 1.19 x 10¹⁰ m

a = 5.79 x 10¹⁰ m