The acceleration due to gravity g is slightly altered by Earth's rotational motion, depending on latitude. At the equator, Earth's centrifugal force, due to its maximum velocity of rotation, acts outward and opposes gravity, reducing the effective value of g slightly. As latitude increases toward thRead more
The acceleration due to gravity g is slightly altered by Earth’s rotational motion, depending on latitude. At the equator, Earth’s centrifugal force, due to its maximum velocity of rotation, acts outward and opposes gravity, reducing the effective value of g slightly. As latitude increases toward the poles, the rotational velocity decreases, and the centrifugal force decreases.
At the poles, centrifugal force is negligible, and g is at its maximum value. Therefore, g is lowest at the equator and increases gradually as one moves toward the poles.
Latitude at a place measures how far north or south it is from the Earth’s equator. It’s expressed in degrees, starting at 0° at the equator and going up to 90° at the North and South Poles. Locations in the Northern Hemisphere have positive latitudes, while those in the Southern Hemisphere have negRead more
Latitude at a place measures how far north or south it is from the Earth’s equator. It’s expressed in degrees, starting at 0° at the equator and going up to 90° at the North and South Poles. Locations in the Northern Hemisphere have positive latitudes, while those in the Southern Hemisphere have negative latitudes.
These imaginary lines, called parallels, run horizontally around the globe. Latitude helps pinpoint a location on Earth and also influences the climate and sunlight a region gets throughout the year, playing a key role in geography and navigation.
The orbital period of a satellite depends on the radius of its orbit and the mass of the central body, such as Earth, but it is independent of the satellite's mass. This means that whether the satellite is small or large, its orbital period remains unchanged as long as the orbital radius and the cenRead more
The orbital period of a satellite depends on the radius of its orbit and the mass of the central body, such as Earth, but it is independent of the satellite’s mass. This means that whether the satellite is small or large, its orbital period remains unchanged as long as the orbital radius and the central body’s mass remain constant. This principle highlights that the motion of a satellite is governed by gravitational forces and does not rely on the satellite’s own mass, making it a fundamental aspect of orbital mechanics.
T = 2π√((R + h)³ / GM),
Clearly, T does not depend on the mass m of the satellite.
Johannes Kepler, a renowned 17th-century astronomer, discovered the fundamental laws of planetary motion, which revolutionized our understanding of the solar system. His first law states that planets orbit the Sun in elliptical paths with the Sun at one focus. The second law, or the law of equal areRead more
Johannes Kepler, a renowned 17th-century astronomer, discovered the fundamental laws of planetary motion, which revolutionized our understanding of the solar system. His first law states that planets orbit the Sun in elliptical paths with the Sun at one focus.
The second law, or the law of equal areas, explains that a planet sweeps out equal areas in its orbit in equal times, indicating varying orbital speeds. His third law establishes a relationship between the orbital period and the distance of a planet from the Sun, revealing a consistent mathematical pattern. These laws laid the foundation for modern celestial mechanics.
A body orbits the Earth at a mean radius that is twice the distance of the parking orbit of a geostationary satellite. According to Kepler's third law, the orbital period of a body increases as the radius of its orbit becomes larger. In this case, the greater radius results in a longer orbital perioRead more
A body orbits the Earth at a mean radius that is twice the distance of the parking orbit of a geostationary satellite. According to Kepler’s third law, the orbital period of a body increases as the radius of its orbit becomes larger. In this case, the greater radius results in a longer orbital period. The body’s period is determined to be approximately 2√2 days, highlighting how the distance from the central body influences the time taken for one complete revolution around the Earth. This demonstrates the proportional relationship between orbital radius and time period.
Explain how is the acceleration due to gravity affected at a latitude due to the rotational motion of the earth.
The acceleration due to gravity g is slightly altered by Earth's rotational motion, depending on latitude. At the equator, Earth's centrifugal force, due to its maximum velocity of rotation, acts outward and opposes gravity, reducing the effective value of g slightly. As latitude increases toward thRead more
The acceleration due to gravity g is slightly altered by Earth’s rotational motion, depending on latitude. At the equator, Earth’s centrifugal force, due to its maximum velocity of rotation, acts outward and opposes gravity, reducing the effective value of g slightly. As latitude increases toward the poles, the rotational velocity decreases, and the centrifugal force decreases.
See lessAt the poles, centrifugal force is negligible, and g is at its maximum value. Therefore, g is lowest at the equator and increases gradually as one moves toward the poles.
Define latitude at a place.
Latitude at a place measures how far north or south it is from the Earth’s equator. It’s expressed in degrees, starting at 0° at the equator and going up to 90° at the North and South Poles. Locations in the Northern Hemisphere have positive latitudes, while those in the Southern Hemisphere have negRead more
Latitude at a place measures how far north or south it is from the Earth’s equator. It’s expressed in degrees, starting at 0° at the equator and going up to 90° at the North and South Poles. Locations in the Northern Hemisphere have positive latitudes, while those in the Southern Hemisphere have negative latitudes.
See lessThese imaginary lines, called parallels, run horizontally around the globe. Latitude helps pinpoint a location on Earth and also influences the climate and sunlight a region gets throughout the year, playing a key role in geography and navigation.
A body is projected from earth’s surface to become its satellite. Its time period of revolution will not depend upon
The orbital period of a satellite depends on the radius of its orbit and the mass of the central body, such as Earth, but it is independent of the satellite's mass. This means that whether the satellite is small or large, its orbital period remains unchanged as long as the orbital radius and the cenRead more
The orbital period of a satellite depends on the radius of its orbit and the mass of the central body, such as Earth, but it is independent of the satellite’s mass. This means that whether the satellite is small or large, its orbital period remains unchanged as long as the orbital radius and the central body’s mass remain constant. This principle highlights that the motion of a satellite is governed by gravitational forces and does not rely on the satellite’s own mass, making it a fundamental aspect of orbital mechanics.
T = 2π√((R + h)³ / GM),
See lessClearly, T does not depend on the mass m of the satellite.
Kepler discovered
Johannes Kepler, a renowned 17th-century astronomer, discovered the fundamental laws of planetary motion, which revolutionized our understanding of the solar system. His first law states that planets orbit the Sun in elliptical paths with the Sun at one focus. The second law, or the law of equal areRead more
Johannes Kepler, a renowned 17th-century astronomer, discovered the fundamental laws of planetary motion, which revolutionized our understanding of the solar system. His first law states that planets orbit the Sun in elliptical paths with the Sun at one focus.
See lessThe second law, or the law of equal areas, explains that a planet sweeps out equal areas in its orbit in equal times, indicating varying orbital speeds. His third law establishes a relationship between the orbital period and the distance of a planet from the Sun, revealing a consistent mathematical pattern. These laws laid the foundation for modern celestial mechanics.
A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a geostationary satellite, the period of body is
A body orbits the Earth at a mean radius that is twice the distance of the parking orbit of a geostationary satellite. According to Kepler's third law, the orbital period of a body increases as the radius of its orbit becomes larger. In this case, the greater radius results in a longer orbital perioRead more
A body orbits the Earth at a mean radius that is twice the distance of the parking orbit of a geostationary satellite. According to Kepler’s third law, the orbital period of a body increases as the radius of its orbit becomes larger. In this case, the greater radius results in a longer orbital period. The body’s period is determined to be approximately 2√2 days, highlighting how the distance from the central body influences the time taken for one complete revolution around the Earth. This demonstrates the proportional relationship between orbital radius and time period.
See less