The motion of our planet in outer space can be characterized by two types of rotation: around its own axis and around the sun. This article discusses the concept of angular velocity, provides the necessary formulas for calculating this quantity, and also calculates the speed of the angular rotation of the Earth around its axis and around our star.
What is angular rotation speed?
When considering the movement of a body in space over long distances, then, as a rule, its size is neglected. In this case, the concepts of the path and the speed of its movement are introduced. If the problem of the motion of a body around a certain point or axis of rotation is solved, then the distance traveled is always equal to the length of the corresponding circle, and the linear velocity of movement is replaced by using the angular velocity.
The angular velocity of rotation is the angle by which the body rotates around the corresponding axis per unit time. Based on this definition, the unit of measurement of the magnitude under consideration will be radians per second (rad / s). You can also use degrees per second (Λ / s). The angular velocity is denoted by the Greek letter omega Ο.
Basic formulas
Before moving on to the question of what the angular velocity of the Earth is, you should get acquainted with the basic formulas that describe this quantity.
As you know, the angular measure of the entire circle is 360 Λ or 2 Γ Ο radians, where Ο = 3.1416. If the body makes a complete revolution around the axis in time T, then we can write the following expression:
Ο = 2 Γ Ο / T = 2 Γ Ο Γ f.
Time T is called the period of revolution, and the value f = 1 / T shows how many revolutions the body will make per unit of time, that is, it characterizes the frequency of its rotation.
Another important formula for angular velocity is an expression combining linear velocity and radius of rotation:
Ο = v / r.
If we check the unit of measurement Ο in this expression, then we get the same radians per second (s -1 ). The formula shows that the smaller the distance from the axis of rotation to the body (r), and the greater its linear speed (v), the greater will be Ο.
From this formula, one can easily express the quantity v: v = Ο Γ r. Since the angular velocity is constant for some body under consideration, those points that are further from the axis of rotation will move faster.
We use the considered formulas and concepts to determine the speed of the angular rotation of the Earth around the axis and around the Sun.
The rotation of our planet around an axis
Everyone knows that the planet on which he lives rotates around his axis, and the equatorial plane of the Earth is inclined at an angle of 23 Β° to the plane of the ecliptic.
How to calculate the angular velocity of rotation around its axis of the Earth? To do this, you can use absolutely any of the formulas that were given above. Since we know that one revolution around the axis occurs in 24 hours, then for the calculation we should use an expression with a period T. We get:
Ο = 2 Γ Ο / T = 2 Γ 3.1416 / (24 Γ 3600) = 7.27 Γ 10 β5 rad / s.
Here, the value of the period T was converted to seconds. The resulting value is small.
It is of interest to calculate at what linear speed the points on the planetβs surface move at latitude 0Λ (equator). The equatorial radius of the Earth is 6,378,000 m. Substituting this value in the formula for speed, we get:
v = Ο Γ r = 7.27 Γ 10 -5 Γ 6 378 000 = 463.8 m / s = 1670 km / h.
The obtained value is large in comparison with the speeds that we observe in life. A person does not feel this speed, because he rotates with the air and soil under his feet at the same speed, that is, he is resting relative to them.
The considered rotation of the Earth leads not only to the appearance of the phenomenon of day and night, but also to the appearance of the so-called Coriolis force, which affects some Earth processes, for example, changes the direction of the winds.
Earth rotation in its orbit
We now calculate the angular velocity of the Earth's rotation around the Sun. To do this, we use the following data: the exact value of the sidereal period of revolution of our planet in orbit is 365 days 6 hours 9 minutes and 9.7632 seconds, that is, T = 31558149.7632 seconds. Now you can use the formula:
Ο = 2 Γ Ο / T = 2 Γ 3.1416 / (31558149.7632) = 1.991 Γ 10 -7 rad / s.
That is, the angular orbital velocity of our planet is less by 1.5 orders of magnitude than the corresponding value for rotation around its own axis. We calculate the linear velocity, given that the average radius of the orbit is 149 597 871 000 meters:
v = Ο Γ r = 1.991 Γ 10 -7 Γ 149 597 871 000 = 29784.8 m / s = 107 225 km / h.
With this tremendous speed, our planet moves in outer space around the Sun.
The existence of the seasons in the Northern and Southern hemispheres is associated with the orbital motion of the planet and the inclination of its axis.