Motion of Celestial Bodies
The motion of celestial bodies such as the moon, the earth, other planets have been a subject of significant interest for a long time.
A famous Indian astronomer and mathematician, Aryabhata did the in-depth study of these motions.
After that, he proposed a theory of the elliptical path of planets where he stated that all the planets remain stable, and as they come closer to the sun because of attraction, their speed increases proportionately.
He also gave a conclusion in his book Aryabhatiya that the earth revolves around its axis and moves in a circular orbit about the sun and that the moon moves in a circular orbit around the earth.
Movement of Celestial Bodies
A thousand years after Aryabhata, the brilliant combination of Tycho Brahe and Johannes Kepler studied planetary motion in significant detail.
Kepler formulated his important findings in his three laws of planetary motion. They are:
First Law: It states that all planets make an elliptical locus with the sun at a focus.
Second Law: The radius vector, r from the sun to the planet traces equal area in equal intervals of time.
Third Law: This law is also called the law of ellipses. This states that the square of the time period, T of the revolution of a planet is proportional to the cube power of the semi-major axis,r of the ellipse.
T ∝ r3
In the year 1665, an English mathematician, physicist, astronomer, and theologian named Isaac Newton studied the motion of the moon about the earth.
He stated that the laws of nature are the same for earthly and heavenly bodies.
This means all the objects in the universe fall freely under the influence of gravity such that the force acts towards the center of the earth.
The acceleration of a body falling near the earth’s surface = 9.8 ms-2.
He formulated an equation to showcase the force between the earth and the body, i.e.,
F =GmM/r2..(1)
G = Universal gravitational constant whose value = 6.673 x 10-11Nm2/kg2
m = mass of the smaller body, and
M = Mass of a larger body, separated by the square of the distance ‘r.’
Newton further generalized the law by saying that not only the earth but all material bodies in the universe attract each other according to equation (1) with the same value of G.
Motion of Celestial Bodies in the Solar System
All planets orbit in a counterclockwise direction. The inner planets orbit swiftly than the outer planets.
They all move in a path that obeys the laws of motion and the force that controls their motion is the gravity.
The earth is the third planet away from the sun, which takes 365 days to complete one orbit.
Motion of Celestial Bodies in Space
All the heavenly bodies like planets and satellites move in an elliptical orbit due to the attractive force of gravity, their centrifugal motion is balanced by the gravitational attraction.
The elliptical orbit is the elongated or skewed circle.
Instead of having a single center like a circle, ellipses have two centers called foci.
f1 and f2 (in Fig.1 (a)).
[Fig 1 & Fig 2- Image to be added Soon]
For planets in space, the center of the sun is always at the focus as shown in Fig.2.
So the larger is the distance between the two foci, the more elongated the ellipse is.
The amount of elongation of the orbit is given by the eccentricity of the orbit.
A planet like the earth has a low eccentricity where both the foci lie within the sun itself. So, we can say that Earth’s orbit is almost circular.
[Fig 2-Image to be added Soon]
Motion of Celestial Objects in Space
Let’s understand the planetary motion by understanding Kepler's laws.
Where Kepler’s first law states that planets revolve around the sun in elliptical shape with the center of the sun being at one focus as you can in Fig.1 (b). This law is also called the Law of ellipses.
The second law states that an unreal line drawn from the center of a star to the center of a planet traces equal areas in equal time intervals.
This law is also called the law of equal areas.
Third law: It states that the ratio of the squares of the periods of revolution of any two planets is equivalent to the cubes of their mean distances from the sun.
[Image to be added Soon]
This is the law of Harmony’s for each point on an ellipse, the sum of the distances from each focus is a constant equal to the time the major-axis length.
In most planetary systems, the eccentricity is low enough that we can approximate the average distance between the star and the planet which is the major axial length of the orbit.
FAQs on Motion of Celestial Bodies in Space
1. What are celestial bodies?
Celestial bodies are natural objects located in outer space. They include a vast range of objects such as stars, planets, moons, asteroids, comets, and galaxies. The study of their movement, known as celestial mechanics, is a fundamental part of physics and astronomy.
2. How do celestial bodies move in space?
The motion of celestial bodies is primarily governed by the force of gravity. They follow predictable paths called orbits. This motion is a balance between their forward velocity (inertia) and the gravitational pull from a more massive nearby object. For example, planets orbit the Sun, and moons orbit planets, in a continuous state of "falling" sideways that prevents them from either flying away or crashing into the central body.
3. What is the main force responsible for the motion of celestial bodies?
The primary force governing the motion of celestial bodies is gravitational force. This universal force of attraction acts between any two objects with mass. It is the force that keeps planets in orbit around the Sun, moons around planets, and holds entire galaxies together. Without gravity, celestial objects would simply move in straight lines through space.
4. What are Kepler's three laws of planetary motion?
Kepler's three laws describe the motion of planets around the Sun, forming the basis of our understanding of celestial orbits:
- The Law of Orbits: Each planet moves in an elliptical orbit with the Sun located at one of the two foci of the ellipse.
- The Law of Areas: A line connecting a planet to the Sun sweeps out equal areas in equal intervals of time. This implies that planets move faster when they are closer to the Sun.
- The Law of Periods: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit (T² ∝ a³).
5. What is the difference between rotation and revolution for a celestial body?
Rotation refers to the spinning of a celestial body on its own internal axis, which is responsible for the cycle of day and night on planets like Earth. Revolution, in contrast, is the movement of one celestial body in an orbit around another, more massive body. For example, Earth completes one rotation in about 24 hours and one revolution around the Sun in approximately 365.25 days.
6. Why don't planets fall into the Sun if its gravity is constantly pulling them?
Planets do not fall into the Sun because they possess a significant sideways velocity, also known as tangential velocity. This velocity is a remnant from the formation of the solar system. The Sun's gravity constantly pulls the planet inward, changing its direction of travel into a curve, but it isn't strong enough to overcome the planet's forward momentum entirely. This perfect balance between the planet's tendency to move straight (inertia) and the Sun's inward pull results in a stable orbit.
7. Are the orbits of all celestial bodies perfect circles?
No, the orbits of celestial bodies are not perfect circles. According to Kepler's First Law, planets and other objects move in elliptical orbits, with their parent star at one of the two foci. A circle is simply a special case of an ellipse where the two foci merge into one point. While some orbits, like Earth's, are nearly circular, others, such as those of comets and many asteroids, are highly elliptical.
8. How did our understanding of celestial motion change from the geocentric to the heliocentric model?
The understanding of celestial motion underwent a monumental shift from an Earth-centric to a Sun-centric view:
- The Geocentric Model, proposed by ancient thinkers like Aristotle and Ptolemy, placed a stationary Earth at the centre of the universe. All other celestial objects were believed to orbit the Earth.
- The Heliocentric Model, introduced by Copernicus and later proven by the work of Kepler and Galileo, correctly placed the Sun at the centre of the solar system. This model provided a much simpler and more accurate explanation for the observed motions of the planets.
9. What would happen to a planet's orbit if its star suddenly lost half its mass?
If a star were to suddenly lose half its mass, the gravitational force it exerts on its orbiting planets would be instantly halved. The existing sideways velocity of the planets would then be too high for the weakened gravity to maintain a stable orbit. The planets would fly off into new, much larger elliptical or even hyperbolic paths, likely escaping the star's system entirely to become rogue planets in interstellar space.
10. If Earth had two moons, how might that affect its motion and tides?
If Earth had a second moon, the planet's dynamics would become significantly more complex. The gravitational interactions would be far more complicated. Tides would be much higher and more erratic, as they would be influenced by the positions of both moons. Furthermore, the two moons would exert gravitational pulls on each other, which could destabilise their orbits over millions of years, potentially leading to a collision or the ejection of one moon from Earth's system.
