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The motion of celestial bodies in space such as the revolution and rotation of planets, movement of the moon, and other satellites has been of interest for mankind for such a long time. These motions were studied in depth by an Indian mathematician and astronomer called Aryabhata. The celestial bodies move in such a way that they obey the laws of motion even in space. In this article, we will have a look at the motion of celestial bodies in space and Kepler’s law of motion.
Click here for video lecture on Kepler’s planetary laws
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Keyterms: Planets, Moon, Satellites, Space, Celestial bodies, Laws of motion, Sun, Milky way, Galaxy
Also Read: Satellite Communication
Movement of Celestial Bodies
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The branch of science dealing with the motion and movement of the celestial bodies is known as celestial mechanics. These celestial bodies in space usually move in an elliptical or parabolic path. While the paths of the planets are elliptical around the sun, satellites on the other hand move elliptically around the planet.
Our entire solar system comprising the sun and the planets move elliptically around the center of The Milky Way, our galaxy. The paths of the planets and satellites are affected by gravity’s attractive force. The elliptical orbit is in the form of an elongated circle that has two centers, known as foci, instead of one.
Elliptical Orbits
In space, the planets have the center of the sun as one or another focus. The larger the distance between these two foci points, the elongated will be the ellipse. The measure of the elongation of the elliptical orbit is determined by its eccentricity.
Fun Fact: The eccentricity of the Earth is so small that both the focus points of the ellipse exist within the sun only. This is why the orbit of Earth almost appears to be circular.
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Motion of Celestial Bodies in the Solar System
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All the planets in the solar system orbit in a clockwise direction. The inner planets have a more swift motion than the outer ones. The path they follow while moving obeys all the laws of motion and are controlled by the force of gravity. Our Earth being the third planet from the sun takes 365 days to orbit around it. The centrifugal motion of the celestial bodies is balanced by the gravitational force of attraction.
Motion of Earth in Solar System
Also Read: Moon - The Natural Satellite
Kepler’s Laws of Planetary Motion in Space
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Three laws given by Kepler, also known as Kepler’s laws of planetary motion, govern the motion of celestial bodies in space. Our moon moves in an elliptical orbit around the Earth by following Kepler’s laws. These three laws help us determine the time it will take a planet to orbit around the sun or how fast or slow a planet will move at any point in the orbit of the planet.
The three laws are:
- The first law of Kepler states that all the planets make an elliptical orbit with the sun at one of the focus.
The first law of Kepler
- The second law states that r, the radius vector from the sun to the planets traces an equal area in equal time intervals.
The second law of Kepler
- The third law of planetary motion in space states that the square of the time period, denoted by T, of a planet’s revolution, is directly proportional to the cubic power of the semi-major axis of the ellipse denoted by r. This law is also called the law of ellipses.
T ∝ r3
The comets have very large eccentric orbits. Hence, after many years they come really close to the sun and can go beyond the planets’ orbits for many years. Comets move in a parabolic orbit when they come close to the sun and afterward keep going away from it. There are some comets that pass close to the sun only once in their lifetime.
Kepler’s Laws of Planetary Motion in Space
Isaac Newton, a physicist, and an astronomer stated that the laws of nature apply to both the Earth and space. Hence, all celestial bodies freely fall under gravity’s influence in such a way that the force act towards the Earth’s center. The body freely falls near the surface of the Earth with an acceleration of 9.8 ms-2.
Newton emphasized that all celestial bodies including Earth attract each other with a similar value of G. This force between the Earth and the falling body can be calculated by the following equation:
F = GmM/r2
Here, G is the universal gravitational constant whose value is equal to 6.673 x 10-11 Nm2/kg2,
m denotes the smaller body’s mass,
M refers to larger body’s mass, and
The square of r (r2) denotes the distance between these two bodies.
Check Out Video Lecture on Kepler’s Laws of Planetary Motion
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Things to Remember
- Our entire solar system comprising the sun and the planets move elliptically around the center of The Milky Way, our galaxy.
- These celestial bodies in space usually move in an elliptical or parabolic path.
- The celestial bodies move in such a way that they obey the laws of motion even in space.
- The comets have very large eccentric orbits.
- In space, the planets have the center of the sun as one or another focus
- The branch of science dealing with the motion and movement of the celestial bodies is known as celestial mechanics.
- Kepler’s laws of planetary motion govern the motion of celestial bodies in space.
- The body freely falls near the surface of the Earth with an acceleration of 9.8 ms-2.
Previous Year Questions
- If Earth shrinks, the new day duration is? [APEAPCET]
- The g value for a planet boigger than the earth is? [NEET 2005]
- Calculate the speed of four particles of identical sizes. [JEE Main 2021]
- The ratio of kinetic to potential energy for a moving satellite is? [NEET 2005]
- Calculate the value of g at a height from the earth’ surface. [JKCET 2004]
- Calculate g at a point below the earth’s surface. [APEAPCET]
- Choose the correct for a synchronous relay satellite. [BHU UET]
- What is g at a height half the radius of the earth. [NEET 2020]
- Determine the escape velocity. [NEET 1993]
- Determine the ratio of the time periods. [NEET 1993]
- When satellite is launched at an angle, the escape velocity is. [NEET 1989]
- Determine the relation between G and K. [NEET 2015]
- Question on Geostationary satellite. [BITSAT 2008]
- Find the ratio of escape velocity. [BITSAT 2010]
- Find the speed of the article under gravitation. [VITEEE 2013]
- Find the distance of a given point from moon. [JCECE 2007]
- Calculate the percentage energy needed to shift the satellite. [JKCET 2015]
- Which curve represents total energy variation of satellite. [AMUEEE 2014]
- Relation of the period with the density of an artificial satellite. [JIPMER]
- Determine the relative velocity of approach. [APEAPCET]
Sample Questions
Ques. Define Celestial Objects? (2 marks)
Ans. The objects located outside the atmosphere of the Earth are known as celestial objects. Some examples of celestial bodies include the stars, moon, other planets, etc.
Ques. Why does the moon revolve around the Earth? (1 mark)
Ans. The moon revolves around the Earth due to its gravitational pull. Moon is therefore Earth’s natural satellite.
Ques. What is Kepler’s constant value? (1 mark)
Ans. The third Kepler’s law of planetary motion is expressed through the following equation: T ∝ r3
Here, k is known as Kepler’s constant. The value of the same is 4π2/GM
Ques. What are the three Kepler’s laws of planetary motion in space? (3 marks)
Ans. The three laws given by Kepler are as follows:
- The first law of Kepler states that all the planets make an elliptical orbit with the sun at one of the focus.
- The second law states that r, the radius vector from the sun to the planets traces an equal area in equal time intervals.
- The third law of planetary motion in space states that the square of the time period, denoted by T, of a planet’s revolution, is directly proportional to the cubic power of the semi-major axis of the ellipse denoted by r. This law is often also called as the law of ellipses.
T ∝ r3
Ques. The Moon revolves around the Earth in a time period of 27.3 days. If we know that the distance of the moon from the Earth is 3.85 x 105 km. Calculate the acceleration for the same. (3 marks)
Ans. We are given that r is equal to 3.85 x 105 km
and T is 27.3 days
The formula for angular acceleration is:
α = ω2r
ω = 2πT
Hence,
α = (2πT)2.r
= 4π2.r/T2
Putting all the given values in the derived formula, we get
α = 4 x (3.14)2 x ( 3.85 x 105)/(27.3)2
Solving for the given values, we get
α = 0.0027 ms-2
Ques. What would be the case if our Earth had two moons instead of one? (2 marks)
Ans. Having an additional moon would increase the gravitational pull on Earth. This will lead to larger tides. When these bodies collide with each other, their remaining debris is sent to the planets.
Ques. Write down three properties of motion of the Earth in space. (3 marks)
Ans. The properties of Earth’s motion in space are:
- Earth revolves around the Sun in elliptical orbits.
- The planet rotates on its own polar axis.
- The planet Earth smoothly swings as a spinning top that remains unbalanced.
Ques. How and through which factors is the orbital speed of a body affected? (2 marks)
Ans. The orbital speed of a celestial body is affected by the distance that exists between the body around which a planet revolves and the planet itself.
Ques. How is the force between the Earth and a falling body calculated? State the equation. (3 marks)
Ans. Isaac Newton stated that all the celestial bodies including Earth attract each other with some force and with a similar value of G. All celestial bodies freely fall under gravity’s influence in such a way that the force act towards the Earth’s center. This force between the Earth and the falling body can be calculated by the following equation:
F = GmM/r2
In this equation, G refers to the universal gravitational constant whose value is equal to 6.673 x 10-11 Nm2/kg2,
m refers to the smaller body’s mass,
M refers to larger body’s mass, and
The square of r (r2) refers to the distance between these two bodies.
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