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Gravity near Earth's surface is all about the interplay between the G and g. While G is universal, g varies with location and altitude, affecting how objects move and weigh differently across Earth's surface.

Understanding gravity's effects helps us calculate celestial body masses and explains phenomena like and tides. It's crucial for grasping how objects behave on Earth and in space, from weighing less at the equator to achieving .

Gravitation Near Earth's Surface

Gravitational constant vs acceleration

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  • Gravitational constant GG measures the strength of gravitational force between two objects (Earth and an object on its surface)
  • Acceleration due to gravity gg quantifies the acceleration experienced by objects due to Earth's gravitational pull near its surface (9.8 )
  • relates GG and gg: g=GMERE2g = \frac{GM_E}{R_E^2}
    • MEM_E represents
    • RER_E represents
  • GG is a universal constant (6.67 × 10⁻¹¹ ) while gg varies with location and altitude
  • The describes the strength and direction of the gravitational force at any point in space

Mass calculation of celestial bodies

  • Calculate the mass of using gg and radius RR
  • Rearrange Newton's Law of Universal Gravitation to solve for mass MM: M=gR2GM = \frac{gR^2}{G}
  • Steps to calculate mass:
    1. Measure surface gravitational acceleration gg on the celestial body
    2. Determine radius RR of the celestial body
    3. Substitute values of gg, RR, and GG into the equation M=gR2GM = \frac{gR^2}{G}
  • This method allows for estimating the mass of planets, moons, and other celestial objects (Mars, Jupiter's moon Europa)

Variations in surface gravity

  • Value of gg varies slightly based on geographical location and Earth's rotation
  • causes gg to be slightly greater at poles compared to equator (0.5% difference)
    • Due to Earth's being slightly flattened at poles
  • causes gg to decrease with increasing altitude above Earth's surface
    • Distance from Earth's center increases, reducing gravitational acceleration
  • Earth's rotation creates small opposing gravitational force
    • Effect is greatest at equator (reduces gg by 0.3%) and zero at poles
  • These variations in gg affect the of objects at different locations (person weighs slightly less at equator than at poles)

Gravitational effects and motion

  • occurs when an object is subject only to the force of gravity, resulting in an acceleration of gg
  • is the minimum speed an object needs to overcome Earth's gravitational pull and escape its orbit
  • are caused by differences in gravitational pull on different parts of an object, leading to deformation and tidal effects on Earth

Key Terms to Review (25)

Acceleration Due to Gravity: Acceleration due to gravity, often denoted as 'g', is the acceleration experienced by an object due to the Earth's gravitational pull. This constant acceleration affects the motion of objects near the Earth's surface, influencing various physical phenomena such as free fall, mass, weight, and gravitational fields.
Altitude Dependence: Altitude dependence refers to the way in which the gravitational field and its effects vary with changes in elevation or distance from the Earth's surface. This concept is particularly important in the study of gravitation near the Earth's surface.
Apparent weight: Apparent weight is the normal force exerted by a surface on an object, which can differ from the object's true weight due to acceleration. It may be perceived differently in scenarios like elevators or free-fall.
Celestial Bodies: Celestial bodies are objects in the universe that exist outside of Earth's atmosphere, such as stars, planets, moons, asteroids, and comets. These objects are the focus of the study of astronomy and play a crucial role in understanding the structure and evolution of the universe.
Centrifugal force: Centrifugal force is a fictitious force perceived in a rotating reference frame, directed outward from the axis of rotation. It arises due to the inertia of an object moving in a curved path.
Centrifugal Force: Centrifugal force is an apparent force that acts on an object moving in a circular path, directing the object away from the center of the circle. It is a result of the object's inertia, which causes it to resist changes in its direction of motion.
Earth's Mass: Earth's mass is the total amount of matter that makes up the planet Earth. It is a fundamental property of the Earth that determines its gravitational pull and influences various physical phenomena on its surface.
Earth's Radius: The Earth's radius is the distance from the center of the Earth to its surface, representing the size and scale of our planet. This fundamental measurement is crucial in understanding the Earth's gravitational field and its effects on objects near the surface.
Escape velocity: Escape velocity is the minimum speed an object must have to break free from a celestial body's gravitational influence without further propulsion. It depends on the mass and radius of the celestial body.
Escape Velocity: Escape velocity is the minimum speed required for an object to break free of a planet or moon's gravitational pull and enter into space without being pulled back down. This concept is crucial in understanding the motion of objects under the influence of gravity.
Free fall: Free fall is the motion of an object under the influence of gravitational force only. It neglects air resistance and assumes a uniform acceleration due to gravity.
Free Fall: Free fall is a state of motion where an object is falling under the sole influence of gravity, without any other external forces acting upon it. This term is closely connected to the topics of motion with constant acceleration, projectile motion, Newton's second law, and gravitational effects near Earth's surface.
Gravitational Constant: The gravitational constant, denoted as 'G', is a fundamental physical constant that describes the strength of the gravitational force between two objects. It is a crucial parameter in understanding the laws of gravitation and the motion of objects under the influence of gravity.
Gravitational field: A gravitational field is a region of space surrounding a mass where another mass experiences a force due to gravity. It is represented by the gravitational field strength, denoted as $g$.
Gravitational Field: A gravitational field is a region of space surrounding a massive object, where the force of gravity is exerted on other objects. It describes the strength and direction of the gravitational force at every point in space, allowing the prediction of the motion of objects within that field.
International Space Station: The International Space Station (ISS) is a large spacecraft in low Earth orbit, serving as a microgravity and space environment research laboratory. It orbits Earth at an average altitude of approximately 400 km.
Latitude Dependence: Latitude dependence refers to the variation in the strength of Earth's gravitational field as a function of the geographic latitude. This phenomenon arises due to the oblate spherical shape of the Earth and its rotation, which causes differences in the acceleration due to gravity at different latitudes.
M/s²: The unit m/s² represents meters per second squared, which measures acceleration in physics. This unit indicates how much the velocity of an object changes per second. Acceleration can be average or instantaneous, and it plays a critical role in understanding motion under the influence of forces, such as gravity, especially near Earth’s surface.
N·m²/kg²: N·m²/kg² is a unit that represents the gravitational field strength, or the acceleration due to gravity, at a specific location near the Earth's surface. This unit is commonly used in the context of understanding gravitational forces and their effects on objects within the Earth's gravitational field.
Newton's Law of Universal Gravitation: Newton's Law of Universal Gravitation is a fundamental principle that describes the attractive force between any two objects with mass. It states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Oblate Shape: An oblate shape, also known as an oblate spheroid, is a three-dimensional geometric shape that is flattened at the poles and bulging at the equator, resembling the shape of a squashed sphere or an oblate ellipsoid. This shape is often used to describe the form of rotating celestial bodies, such as planets, moons, and stars, that are influenced by the effects of gravity and centrifugal forces.
Surface gravitational acceleration: Surface gravitational acceleration is the acceleration experienced by an object due to the force of gravity acting on it at the surface of a celestial body, such as Earth. This acceleration varies slightly depending on location due to factors like altitude and the Earth's rotation, but it is typically approximated as 9.81 m/s² near sea level. Understanding this concept is crucial because it provides insights into how objects move under the influence of gravity and helps explain various physical phenomena related to motion.
Tidal Forces: Tidal forces are the gravitational forces exerted by celestial bodies, such as the Moon and the Sun, that cause the periodic rise and fall of the Earth's oceans, known as tides. These forces arise from the difference in the gravitational pull on different parts of an object, creating a stretching or deforming effect.
Universal gravitational constant: The universal gravitational constant, denoted as $G$, is a fundamental physical constant that quantifies the strength of the gravitational force between two masses. Its value is approximately $6.674 \times 10^{-11} \text{Nm}^2\text{kg}^{-2}$.
Weight: Weight is the force exerted on an object due to the pull of gravity. It is a measure of the gravitational force acting on an object, and it varies depending on the object's mass and the strength of the gravitational field it is in.
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Glossary
Glossary
13.3 Gravitational Potential Energy and Total Energy