Structure of Adhaar Number

The gravity discussion:-

1. The gravity is caused by space time curvature. In this way should earth not stick with the sun?

2. Which celestial body will revolve around an other celestial body is decided by space -time curve ?

3. If earth has started revolving around sun by itself, so what can be said about law of conservation of energy?

4. Why is there no loss in initial energy of earth during the revolution around the sun 

5. Why is the path of earth is elliptical?why not circular?

6. Varying speed causes elliptical path or elliptical path causes varying speed?

7. Why does earth speed varies? Does it's mass changes?

8. Does space time curvature decide the path,  elliptical?

9. Every celestial body in space time curvature follow elliptical path?

10. Does kinetic energy of earth changes?

11. What involves in the total energy of earth and sun system?

12. Why does earth recedes and approaches the sun during its revolution?

13. Total energy of earth and sun system is zero?

14. Magnitude of GPE is always greater than KE?

15. If earth were to be removed from solar system. What will happen?

16. What will happen with moon in this scenario?

1. The gravity is caused by space time curvature. In this way earth should stick with the sun.

Gravity is indeed caused by the curvature of spacetime created by massive objects like the Sun. Earth orbits the Sun because it follows the curved path created by this gravitational interaction.

Earth's orbit around the Sun is precisely what keeps it from falling into the Sun due to gravity. The combination of Earth's forward motion and the gravitational pull of the Sun creates a stable orbit. Without this motion, Earth would indeed be pulled towards the Sun.

2. Which celestial body will revolve around which celestial body is decided by space -time curvature ?

The curvature of spacetime determines the paths that celestial bodies follow. In our solar system, the gravitational influence of the Sun causes planets like Earth to orbit around it. Similarly, moons orbit planets due to the curvature of spacetime created by the planet's mass. So, the distribution of mass and the resulting curvature of spacetime determine how objects move in space.

3. If earth has started revolving around sun by itself, so what can be said about law of conservation of energy?

If Earth were to suddenly start revolving around the Sun without any external force acting upon it, it would violate the law of conservation of energy. According to this law, the total energy of a closed system remains constant over time. In this scenario, Earth would need an initial input of energy to initiate its motion around the Sun. Without such input, it would contradict the principle of energy conservation.

The motion of Earth around the Sun became possible through the initial conditions of the solar system's formation. When the solar system formed from a rotating cloud of gas and dust, the gravitational forces between particles caused them to clump together, forming larger and larger objects. Eventually, these processes led to the formation of the Sun and the planets, with each object inheriting some of the original angular momentum of the cloud. This angular momentum causes objects to move in orbits around each other without violating the law of conservation of energy, as the energy required for their motion was present from the beginning of the system's formation.

The energy that maintains Earth's revolution around the Sun comes from its initial kinetic energy and gravitational potential energy, which were set in motion during the formation of the solar system. Once set in motion, Earth continues to orbit the Sun due to the gravitational attraction between the two bodies. This gravitational force provides the centripetal force needed to keep Earth in its orbit without any additional energy input. Therefore, the energy required for Earth's orbit is primarily provided by its initial conditions and the gravitational interaction with the Sun.

4. Why is there no loss in initial energy of earth during the revolution around the sun?

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In the case of Earth's revolution around the Sun, the initial kinetic energy and gravitational potential energy of Earth, acquired during the formation of the solar system, are conserved throughout its orbit. 

As Earth orbits the Sun, its kinetic energy (due to its motion) and gravitational potential energy (due to its position relative to the Sun) may change slightly as it moves through its orbit. However, the total energy of the Earth-Sun system remains constant over time. This is because any changes in kinetic energy are balanced by changes in potential energy, and vice versa, keeping the total energy constant.

In the absence of external forces (such as friction or significant gravitational interactions with other celestial bodies), Earth's orbit around the Sun remains stable, and there is no loss of initial energy.

The conservation of energy principle is a fundamental concept in physics that is exact within the framework of classical mechanics, where external factors such as friction and non-conservative forces are negligible. In the case of Earth's orbit around the Sun, assuming no significant external influences, the conservation of energy is an exact principle. 

However, in more complex scenarios involving factors like relativistic effects, quantum mechanics, or interactions with other celestial bodies, the conservation of energy may need to be considered more carefully and could lead to approximations or adjustments.

5. Why is the path of earth is elliptical?why not circular?

The path of Earth around the Sun is elliptical rather than perfectly circular due to the gravitational interaction between Earth and the Sun. According to Kepler's laws of planetary motion, planets orbit the Sun in elliptical paths with the Sun at one of the two foci of the ellipse.

The eccentricity of Earth's orbit (how elongated the ellipse is) is relatively small, so its orbit appears almost circular. However, it's not a perfect circle. This elliptical shape is a result of the gravitational pull of the Sun, which causes the speed of Earth to vary slightly throughout its orbit. At the point of closest approach to the Sun (perihelion), Earth moves slightly faster, and at the farthest point (aphelion), it moves slightly slower. This variation in speed causes the orbit to be an ellipse rather than a perfect circle.

6. Varying speed causes elliptical path or elliptical path causes varying speed?

The varying speed of Earth in its orbit is a consequence of its elliptical path rather than the other way around. 

The gravitational force exerted by the Sun on Earth causes it to accelerate as it gets closer to the Sun (at perihelion) and decelerate as it moves farther away (at aphelion). This variation in speed is a direct result of the elliptical shape of Earth's orbit. 

In other words, the elliptical path of Earth around the Sun leads to varying speeds because of the changing gravitational force exerted by the Sun at different points in its orbit.

7. Why does earth speed varies? Does it's mass changes?

The speed of Earth varies in its orbit around the Sun due to the gravitational force exerted by the Sun. According to Newton's law of universal gravitation, the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. 

As Earth moves in its elliptical orbit around the Sun, the distance between Earth and the Sun changes. When Earth is closer to the Sun (at perihelion), the gravitational force is stronger, causing Earth to accelerate. Conversely, when Earth is farther from the Sun (at aphelion), the gravitational force is weaker, causing Earth to decelerate.

The mass of Earth itself does not change significantly during its orbit around the Sun, so the variation in speed is primarily due to changes in the distance between Earth and the Sun.

8. Does space time curvature decide the path elliptical?

Yes, the curvature of spacetime, as described by Einstein's theory of general relativity, influences the shape of planetary orbits. In the case of Earth's orbit around the Sun, the curvature of spacetime caused by the Sun's mass dictates that Earth follows an elliptical path rather than a perfect circle.

The mass of the Sun causes spacetime to curve around it, and objects like Earth follow the curved paths created by this curvature. These paths are determined by the balance between the gravitational force pulling the object inward and its velocity trying to carry it forward in a straight line. In the case of Earth, this results in an elliptical orbit around the Sun. So, the curvature of spacetime indeed plays a crucial role in determining the shape of planetary orbits.

9. Every celestial body in space time curvature follow elliptical path?

Not necessarily. While the curvature of spacetime does influence the paths that celestial bodies follow, not all orbits are necessarily elliptical. The shape of an orbit depends on various factors such as the distribution of mass in the system, the initial conditions of the objects, and the presence of other gravitational influences.

In the case of our solar system, most planetary orbits are nearly elliptical, but they can deviate slightly due to perturbations from other planets, moons, or even passing asteroids and comets. Additionally, in systems with multiple massive bodies or in extreme gravitational environments like those near black holes, orbits can take on more complex shapes, including spirals or even chaotic trajectories.

So while the curvature of spacetime influences the paths of celestial bodies, the exact shape of an orbit can vary depending on the specific dynamics of the system.

The solar system is a complex and dynamic system governed by the interplay of gravitational forces between celestial bodies. While we often simplify it to basic models, the reality is much more intricate.

The gravitational interactions between the Sun, planets, moons, asteroids, comets, and other celestial objects create a rich tapestry of orbits, resonances, and interactions. These interactions can lead to phenomena like planetary perturbations, gravitational tugs, resonances, and even orbital resonances, where the gravitational pull of one body affects the orbit of another.

Understanding and modeling the behavior of the solar system requires sophisticated mathematical and computational tools. Even with our current understanding, there are still many mysteries and complexities yet to be fully explored and understood.

The concept of Earth's elliptical orbit and its varying speed can indeed be challenging to grasp since our everyday experiences often don't involve such celestial mechanics. However, it might help to think of it in terms of forces and motion.

Imagine swinging a ball on a string around in a circle. If you let the string out a bit, the ball will move faster, and if you pull it in, the ball will slow down. This is similar to how Earth moves around the Sun. When Earth is closer to the Sun, it moves faster due to the stronger gravitational pull. As it moves farther away, the gravitational pull weakens, causing Earth to slow down.

Similarly, the elliptical shape of Earth's orbit is a result of the balance between the gravitational force pulling Earth towards the Sun and Earth's velocity trying to carry it forward in a straight line. This balance creates an orbit that is not a perfect circle but an ellipse.

While these concepts might seem abstract, they are fundamental to our understanding of the dynamics of celestial bodies in space. 

10. The kinetic energy of Earth changes as it moves in its orbit around the Sun. 

When Earth is closer to the Sun (at perihelion), it moves faster, so its kinetic energy is higher. Conversely, when Earth is farther from the Sun (at aphelion), it moves slower, resulting in lower kinetic energy. 

This variation in kinetic energy is a consequence of the changing gravitational force between Earth and the Sun as Earth moves through its elliptical orbit.

The law of conservation of energy still holds in the case of Earth's orbit around the Sun, despite the variation in kinetic energy. This is because the total energy of the Earth-Sun system remains constant over time.

While Earth's kinetic energy changes as it moves through its orbit, its gravitational potential energy also changes in the opposite direction. When Earth is closer to the Sun and has higher kinetic energy, it also has lower potential energy. Conversely, when Earth is farther from the Sun and has lower kinetic energy, it has higher potential energy.

The sum of Earth's kinetic energy and gravitational potential energy at any point in its orbit remains constant, in accordance with the law of conservation of energy. Therefore, while energy is transferred between kinetic and potential forms as Earth moves in its orbit, the total energy of the system remains unchanged.

11. Total energy of Earth-Sun system

The total energy of the Earth-Sun system involves both kinetic energy and gravitational potential energy?

1. Kinetic Energy: This is the energy associated with the motion of the objects. For the Earth, it's the energy related to its orbital motion around the Sun. For the Sun, it's the energy related to its own rotation and any motion it may have within the galaxy.

2. Gravitational Potential Energy: This is the energy associated with the gravitational interaction between the Earth and the Sun. It depends on the masses of the objects and their separation distance. As Earth orbits the Sun, its distance from the Sun changes, altering its gravitational potential energy. 

The gravitational potential energy (GPE) between two objects can be calculated using the formula:

GPE = -GMm/r

Where:

- G is the gravitational constant 6.674 x 10^{-11} N m²/kg²)

- M and m are the masses of the two objects (in kilograms)

- r is the distance between the centers of the two objects (in meters)

The negative sign indicates that the gravitational potential energy is a negative quantity, meaning it is bound and decreases as the distance between the objects increases.

As the distance r between the two objects increases, the gravitational potential energy (GPE) becomes less negative, approaching zero. This means that the gravitational potential energy is increasing, indicating that the objects are moving farther apart in the gravitational field.

In simpler terms, as the objects move farther apart, they have the potential to do more work on each other due to gravity. Therefore, the gravitational potential energy increases with increasing distance between the objects.

The total energy of the Earth-Sun system is the sum of the kinetic energy and gravitational potential energy of both the Earth and the Sun. Despite the variations in individual energies as Earth moves in its orbit, the total energy of the system remains constant over time according to the law of conservation of energy.

12. Why does earth recedes and approaches the sun during its revolution?

The Earth's orbit around the Sun is not perfectly circular; it's elliptical. This means that Earth's distance from the Sun varies throughout its orbit. 

When Earth is closest to the Sun in its orbit, it's at a point called perihelion. At perihelion, Earth is approximately 147 million kilometers (91.5 million miles) away from the Sun. 

Conversely, when Earth is farthest from the Sun in its orbit, it's at a point called aphelion. At aphelion, Earth is approximately 152 million kilometers (94.5 million miles) away from the Sun.

The variation in Earth's distance from the Sun is due to the elliptical shape of its orbit. This elliptical shape causes Earth to experience changes in its orbital speed as it moves around the Sun. When Earth is closer to the Sun (at perihelion), it moves faster in its orbit. When it's farther from the Sun (at aphelion), it moves slower.

So, Earth recedes and approaches the Sun during its revolution because of its elliptical orbit and the resulting changes in orbital speed and distance.

13. Total energy of earth and sun system is zero?

In the context of the Earth-Sun system, the total energy is not zero. The total energy of the Earth-Sun system is negative, indicating that it's a bound system. This negative tonergy's of ergy reflects the fact that Earth is gravitationally bound to the Sun and is in a stable orbit around it.

The total energy of the system is the sum of the kinetic energy and gravitational potential energy of both the Earth and the Sun. Despite variations in individual energies as Earth orbits the Sun, the total energy of the system remains constant over time, in accordance with the law of conservation of energy.

So, while the total energy is negative, it's not zero. It represents the overall energy state of the Earth-Sun system, with gravitational potential energy contributing to the negative total energy.

14. Magnitude GPE is always greter than KE?

Not necessarily. In the Earth-Sun system, the gravitational potential energy (GPE) is indeed typically greater in magnitude than the kinetic energy (KE) of either the Earth or the Sun individually, because the gravitational potential energy is negative (indicating a bound system), while kinetic energy is positive.

However, the exact relationship between GPE and KE depends on the specific configuration and conditions of the system. For example, at certain points in Earth's orbit, such as perihelion (the closest point to the Sun), the kinetic energy may be relatively high compared to the gravitational potential energy. Conversely, at aphelion (the farthest point from the Sun), the gravitational potential energy is relatively high compared to the kinetic energy.

Overall, while GPE is typically greater in magnitude than KE in the Earth-Sun system, the specific relationship between the two energies varies depending on factors such as the distance between the objects and their velocities.

The total energy E of an object in motion, such as the Earth orbiting the Sun, is the sum of its kinetic energy K and its gravitational potential energy U. 

E = K + U

The formula for kinetic energy, K is:

K = (1/2) m v^2

where:

- m is the mass of the object,

- v is the velocity of the object.

The formula for gravitational potential energy, U is:

U = - G M m/r

where:

- G is the gravitational constant 6.674 x 10^{-11} N m²/kg²),

- M is the mass of the larger object (e.g., the Sun),

- m is the mass of the smaller object (e.g., the Earth),

- r is the distance between the centers of the two objects.

So, the total energy of an object in motion is the sum of its kinetic energy and its gravitational potential energy, taking into account their respective formulas.

15. If earth were to be removed from solar system. What will happen?

If Earth were to be suddenly removed from the solar system, several significant consequences would ensue:

Effects on Earth

1. Gravitational Influence: Earth's removal would disrupt the gravitational balance in the solar system. Other planets and celestial bodies might experience slight changes in their orbits due to the redistribution of mass.

2. Solar System Dynamics: While the Sun's gravity is the dominant force, the absence of Earth's mass would slightly alter the center of mass (barycenter) of the solar system, but this change would be minimal given the Sun's massive size compared to Earth.

Effects on Life and Environment

1. Loss of Sunlight: Without the Sun's light and heat, Earth's temperature would plummet, causing catastrophic freezing. Most life forms, which rely on the Sun's energy, would not survive.

2. Atmospheric Changes: The atmosphere would cool and potentially freeze, causing atmospheric gases to precipitate out of the atmosphere, drastically altering the environment.

Effects on Other Planets and the Solar System

1. Orbital Adjustments: The removal of Earth might cause minor perturbations in the orbits of other planets and asteroids, but these changes would likely be small due to the relatively small mass of Earth compared to the Sun.

Cosmic Perspective

1. Solar System Dynamics: While the immediate vicinity arounIf Earth were to be suddenly removed from the solar system, the Moon would experience significant changes as well:

1. Loss of Gravitational Pull: Without Earth's gravitational pull, the Moon would no longer have an object to orbit around.

2. Trajectory Change: The Moon would continue moving in the direction it was heading at the moment of Earth's disappearance, due to its inertia. This path would be influenced by the Sun's gravitational pull.

3. New Orbit: The Moon would likely enter a new orbit around the Sun, becoming a small planet or asteroid-like body in the solar system. Its new orbit would depend on its velocity and position relative to the Sun at the moment of Earth's removal.

4. Gravitational Influences: Other gravitational influences in the solar system, such as from nearby planets, could perturb the Moon's new orbit, potentially leading to further changes over time.

In summary, the Moon would no longer orbit Earth and would instead become an independent object orbiting the Sun.d Earth's former orbit might experience some changes, the overall structure of the solar system would remain largely intact.

In summary, while the immediate consequences for Earth and any life on it would be catastrophic, the broader solar system would experience relatively minor changes due to the removal of Earth's mass.

16. What will happen with moon in this scenario?

If Earth were to be suddenly removed from the solar system, the Moon would experience significant changes as well:

1. Loss of Gravitational Pull: Without Earth's gravitational pull, the Moon would no longer have an object to orbit around.

2. Trajectory Change: The Moon would continue moving in the direction it was heading at the moment of Earth's disappearance, due to its inertia. This path would be influenced by the Sun's gravitational pull.

3. New Orbit: The Moon would likely enter a new orbit around the Sun, becoming a small planet or asteroid-like body in the solar system. Its new orbit would depend on its velocity and position relative to the Sun at the moment of Earth's removal.

4. Gravitational Influences: Other gravitational influences in the solar system, such as from nearby planets, could perturb the Moon's new orbit, potentially leading to further changes over time.

In summary, the Moon would no longer orbit Earth and would instead become an independent object orbiting the Sun.