9th Class Physics Unit No.5 Gravitation Notes
Force of Gravitation: The force that exists between every pair of bodies in the universe and causes them to attract each other is called the force of gravitation. It is responsible for the falling of objects on Earth and the Moon staying in its orbit.
Law of Universal Gravitation: According to Newton’s law of universal gravitation, every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Proportionality Constant (G): The proportionality constant in the law of gravitation is denoted by G and is called the universal constant of gravitation. Its value is approximately 6.673 × 10^-11 Nm^2/kg^2.
Gravitational Field: The gravitational force per unit mass at a point in space is called the gravitational field strength. It is represented by the symbol ‘g’ and is directed towards the center of the Earth.
Mass of the Earth: The mass of the Earth, denoted by ‘M,’ can be determined by observing the gravitational force between the Earth and a body on its surface. The mass of the Earth is approximately 6 x 10^24 kg.
Variation of g with Altitude: The value of acceleration due to gravity (g) decreases with an increase in altitude. At a height equal to one Earth radius above the surface, g becomes one-fourth of its value on the Earth, and at two Earth radii above, g becomes one-ninth of its value on the Earth.
Artificial Satellites: Artificial satellites are man-made objects that are placed in orbit around the Earth. They revolve around the Earth just like natural satellites, such as the Moon. Communication satellites, used for various purposes like telecommunications and experiments, are examples of artificial satellites.
A satellite requires centripetal force to keep it moving around the Earth. The gravitational force of attraction between the satellite and the Earth provides the necessary centripetal force.
Consider a satellite of mass ‘m’ revolving around the Earth at an altitude ‘h’ in an orbit of radius ‘r’ with an orbital velocity ‘v’. The necessary centripetal force required is given by the equation F_c = m * (v^2 / r).
This force is provided by the gravitational force of attraction between the Earth and the satellite and is equal to the weight of the satellite, which is given by F_g = m * g. Thus, F_c = F_g.
Using Newton’s law of universal gravitation, we can equate the centripetal force with the gravitational force: m * (v^2 / r) = (G * M * m) / (R + h)^2.
Solving for the orbital velocity ‘v’, we get v = sqrt((G * M) / (R + h)) where ‘M’ is the mass of the Earth, ‘R’ is the radius of the Earth, and ‘G’ is the universal constant of gravitation.
For satellites revolving close to the Earth, where R >> h, an approximation can be made, and the speed ‘v’ is approximately 8 km/s or 29,000 km/h.
What is meant by the force of gravitation?
The force of gravitation is a fundamental force of nature that exists between any two objects with mass. It is an attractive force that causes objects to be drawn towards each other. The force of gravitation is responsible for keeping planets in orbit around the Sun, moons around planets, and objects on the surface of the Earth. It follows Newton’s law of universal gravitation, which states that every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Do you attract the Earth or the Earth attracts you? Which one is attracting with a larger force? You or the Earth.
Both you and the Earth attract each other with a force of gravitation. According to Newton’s third law of motion, for every action, there is an equal and opposite reaction. So, when you stand on the surface of the Earth, the Earth exerts a gravitational force on you (your weight) pulling you towards the Earth’s center, and you, in turn, exert an equal but opposite gravitational force on the Earth. However, the Earth has a much larger mass compared to you, so the force with which the Earth attracts you is much larger than the force with which you attract the Earth.
What is a field force?
A field force is a type of force that acts on an object even when the objects are not in direct physical contact. These forces act through space and can influence the motion or state of an object from a distance. Gravitational force is an example of a field force, as it acts between two masses without any direct physical contact between them.
Why earlier scientists could not guess about the gravitational force?
Earlier scientists could not guess about the gravitational force because they lacked the necessary experimental evidence and tools to observe and measure the interactions between masses at large distances accurately. The concept of a force of attraction between celestial bodies required a deep understanding of both mechanics and mathematics, which was not fully developed until the time of Isaac Newton.
How can you say that gravitational force is a field force?
Gravitational force is considered a field force because it acts between two masses without the need for physical contact between them. The force of gravitation creates a gravitational field around any mass. When a second mass is brought into this field, it experiences a force of attraction towards the first mass due to the influence of the field. This force acts instantaneously across space, making it a field force.
Explain what is meant by gravitational field strength?
Gravitational field strength is a measure of the gravitational force experienced by a unit mass placed at a certain point in space. It is a vector quantity, and its direction is towards the center of the mass creating the gravitational field. The strength of the gravitational field is determined by the mass of the object creating the field. For example, near the surface of the Earth, the gravitational field strength is approximately 9.8 N/kg.
Why is the law of gravitation important to us?
The law of gravitation is essential to us because it explains the force that keeps celestial bodies in their orbits, governs the motion of planets, moons, and satellites, and is responsible for the weight we feel on the Earth’s surface. Understanding the law of gravitation has allowed humans to explore space, launch satellites, and predict celestial events with accuracy.
Explain the law of gravitation.
The law of gravitation states that every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it is expressed as F = (G * m1 * m2) / r^2, where F is the gravitational force, m1 and m2 are the masses of the objects, r is the distance between their centers, and G is the universal constant of gravitation.
How can the mass of Earth be determined?
The mass of the Earth can be determined by measuring the acceleration due to gravity (g) at its surface and using the formula g = (G * M) / R^2, where M is the mass of the Earth, R is its radius, and G is the universal constant of gravitation. By rearranging the formula, we can find M = (g * R^2) / G.
Can you determine the mass of our moon? If yes, then what do you need to know?
Yes, the mass of the Moon can be determined using the law of gravitation. By measuring the acceleration due to gravity on the Moon’s surface (g_moon) and knowing the radius of the Moon (R_moon), we can use the formula M_moon = (g_moon * R_moon^2) / G to calculate the mass of the Moon.
Why does the value of g vary from place to place?
The value of ‘g’ (acceleration due to gravity) varies from place to place due to differences in the distance from the center of the Earth. ‘g’ is inversely proportional to the square of the distance from the center of the Earth. Therefore, as one moves farther from the Earth’s surface (increasing altitude), the value of ‘g’ decreases.
Explain how the value of g varies with altitude.
The value of ‘g’ decreases with increasing altitude from the Earth’s surface. The gravitational force between the Earth and an object is proportional to the mass of the Earth and inversely proportional to the square of the distance between their centers. As altitude increases, the distance from the center of the Earth increases, causing the force of gravity to weaken, and hence, the value of ‘g’ decreases.
What are artificial satellites?
Artificial satellites are man-made objects launched into space and placed into orbit around celestial bodies, such as planets or moons. They are used for various purposes, including communication, weather monitoring, navigation, Earth observation, and scientific research. Communication satellites, for example, facilitate long-distance communication by relaying signals between ground stations.
How does Newton’s law of gravitation help in understanding the motion of satellites?
Newton’s law of gravitation helps in understanding the motion of satellites by explaining the force of gravity that keeps them in orbit. According to this law, every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For satellites orbiting the Earth, the gravitational force between the satellite and the Earth provides the necessary centripetal force to keep the satellite in its orbit.
On what factors does the orbital speed of a satellite depend?
The orbital speed of a satellite depends on its altitude (distance from the Earth’s surface) and the mass of the celestial body it orbits. The higher the satellite’s altitude, the lower the orbital speed required to maintain its orbit. The mass of the celestial body (e.g., Earth) also affects the orbital speed; larger masses require higher orbital speeds.
Why are communication satellites stationed at geostationary orbits?
Communication satellites are stationed at geostationary orbits because these orbits have a special characteristic. The geostationary orbit is a specific circular orbit above the Earth’s equator, where the satellite’s orbital period matches the Earth’s rotational period (approximately 24 hours). As a result, the satellite appears to remain stationary relative to a fixed point on the Earth’s surface. This characteristic allows communication satellites to maintain constant positions relative to specific ground stations, which is crucial for continuous and reliable communication services.