Gravitational Field | Waec Physics

Gravitational Field

1. A gravitational field is a region where a mass experiences a gravitational force.
2. Gravitational fields are always attractive in nature.
3. The strength of a gravitational field is measured in N/kg or m/s².
4. Gravitational field lines point toward the center of the mass creating the field.
5. Field strength decreases with distance from the source mass.
6. The source of a gravitational field is the mass of an object.
7. Gravitational fields are represented mathematically by $\vec{g} = \frac{\vec{F}}{m}$, where $\vec{F}$ is the gravitational force.
8. Field strength at the Earth’s surface is approximately $9.8N/kg$.
9. Uniform gravitational fields have parallel and equally spaced field lines.
10. Gravitational fields become non-uniform as the distance from the source increases.
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Acceleration Due to Gravity

11. Acceleration due to gravity, $g$, is the acceleration experienced by an object in free fall near a massive body.
12. The value of $g$ at the Earth’s surface is $9.8m/s^2$.
13. $g$ decreases with altitude as $g \propto \frac{1}{r^2}$, where $r$ is the distance from the Earth’s center.
14. The acceleration due to gravity is independent of the mass of the falling object.
15. $g$ is maximum at the Earth’s poles due to the planet’s oblate shape.
16. $g$ is minimum at the equator because of the Earth's rotation.
17. The value of $g$ varies slightly based on local geological structures.
18. On the Moon, $g$ is about $1/6$th that of Earth.
19. On Jupiter, $g$ is approximately $2.5$ times that of Earth.
20. Acceleration due to gravity enables satellite orbits and free fall motion.
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Gravitational Field Intensity (g)

21. Gravitational field intensity $g$ is the force experienced by a unit mass in a gravitational field.
22. It is mathematically expressed as $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the source mass, and $r$ is the distance.
23. The SI unit of $g$ is $N/kg$ or $m/s^2$.
24. Gravitational field intensity is a vector quantity.
25. The direction of $g$ is toward the center of the mass generating the field.
26. Near the Earth’s surface, $g$ is approximately constant.
27. In space, $g$ varies with distance from the mass source.
28. $g$ is used to calculate weight, $W = mg$.
29. Gravitational field intensity determines the motion of celestial objects.
30. $g$ decreases inside a spherical body, such as Earth, as $r$ decreases.
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Gravitational Force Between Two Masses

31. Gravitational force is the attractive force between any two masses.
32. It is described by Newton’s law of gravitation: $F = \frac{Gm_1m_2}{r^2}$.
33. Gravitational force depends on the masses $m_1$ and $m_2$, and the distance $r$ between them.
34. Gravitational force is inversely proportional to the square of the distance.
35. The gravitational force is proportional to the product of the two masses.
36. For small masses like protons and electrons, gravitational force is negligible compared to electromagnetic forces.
37. For large masses like planets and stars, gravitational force dominates interactions.
38. Gravitational force governs planetary orbits and galaxy formation.
39. Gravitational forces between everyday objects are extremely small.
40. Tides on Earth are caused by the gravitational interaction with the Moon and the Sun.
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Masses Include Protons, Electrons, and Planets

41. Gravitational forces between subatomic particles like protons and electrons are negligible due to their tiny masses.
42. In planetary systems, masses like planets and stars generate significant gravitational forces.
43. Protons and electrons interact more strongly via electromagnetic forces than gravitational forces.
44. Planets generate gravitational fields strong enough to shape orbits.
45. Stars like the Sun dominate the gravitational interaction in their respective systems.
46. The gravitational force between two protons is much weaker than the Coulomb force between them.
47. Planetary masses determine orbital speeds and escape velocities.
48. Gravitational interactions between planets lead to phenomena like perturbations.
49. In celestial systems, masses are often treated as point masses for simplicity.
50. The mass of celestial bodies influences gravitational lensing effects.
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Newton’s Law of Gravitation

51. Newton’s law of gravitation states that every mass attracts every other mass with a force proportional to their masses and inversely proportional to the square of the distance between them.
52. The law is expressed as $F = \frac{Gm_1m_2}{r^2}$.
53. It applies universally to all objects with mass.
54. Newton’s law explains both terrestrial and celestial motion.
55. The law assumes instantaneous action at a distance, which was later refined by Einstein’s general relativity.
56. Newton’s law forms the basis for calculating planetary orbits.
57. It governs phenomena like free fall, tides, and satellite motion.
58. The force described by Newton’s law is conservative.
59. Newton’s law works accurately for weak gravitational fields and low velocities.
60. The gravitational constant $G$ was experimentally determined using the Cavendish experiment.
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Universal Gravitational Constant (G)

61. The universal gravitational constant $G$ quantifies the strength of gravitational interaction.
62. The value of $G$ is $6.674 \times 10^{-11} Nm^2/kg^2$.
63. $G$ is a fundamental constant in physics.
64. It appears in Newton’s law of gravitation and other gravitational formulas.
65. The unit of $G$ reflects its role in force calculations.
66. $G$ is the same throughout the universe.
67. Accurate measurements of $G$ are challenging due to its small magnitude.
68. The Cavendish experiment was the first to measure $G$.
69. $G$ is crucial in calculating planetary masses and orbits.
70. Gravitational phenomena on cosmological scales depend on $G$.
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Relationship Between G and g

71. $g$ is derived from $G$ using $g = \frac{GM}{r^2}$.
72. $G$ is a constant, while $g$ varies with location and altitude.
73. $G$ applies universally, while $g$ is specific to a particular mass and location.
74. $g$ can be calculated using $G$ and the mass and radius of the planet.
75. On Earth, $g \approx 9.8m/s^2$ due to $G$ and the Earth’s mass.
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Gravitational Potential and Escape Velocity

76. Gravitational potential is the work done per unit mass to move a mass from infinity to a point in the field.
77. It is expressed as $V = -\frac{GM}{r}$.
78. Gravitational potential is scalar and negative, indicating an attractive force.
79. Escape velocity is the minimum speed required to leave a gravitational field without returning.
80. Escape velocity is calculated using $v_{escape} = \sqrt{\frac{2GM}{r}}$.
81. On Earth, the escape velocity is approximately $11.2km/s$.
82. Escape velocity depends on the mass and radius of the planet or celestial body.
83. Higher mass or smaller radius results in a greater escape velocity.
84. Escape velocity is independent of the mass of the escaping object.
85. Gravitational potential energy at the surface is $U = \frac{-GMm}{r}$.
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Calculation of Escape Velocity

86. Escape velocity from Earth is determined using $v_{escape} = \sqrt{2gR}$, where $R$ is Earth’s radius.
87. For Earth, $g = 9.8m/s^2$ and $R = 6,371km$.
88. Substituting values gives $v_{escape} \approx 11.2km/s$.
89. The calculation assumes no air resistance or other forces.
90. The escape velocity for the Moon is lower due to its smaller mass and radius.
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Additional Insights

91. Escape velocity allows spacecraft to leave a planet’s gravitational influence.
92. Rockets achieve escape velocity using propulsion systems.
93. Gravitational potential determines energy requirements for space missions.
94. Spacecraft in low Earth orbit do not require escape velocity to maintain orbit.
95. Escape velocity is crucial in designing interplanetary missions.
96. Black holes have escape velocities greater than the speed of light.
97. The relationship between gravitational potential and escape velocity explains orbital mechanics.
98. For multi-stage rockets, achieving escape velocity is a stepwise process.
99. Launch windows consider escape velocity and Earth’s rotation for efficiency.
100. Understanding escape velocity aids in satellite deployment beyond geostationary orbit.
101. For smaller celestial bodies like asteroids, escape velocities are significantly lower.
102. Escape velocity calculations assume an idealized spherically symmetric mass.
103. Gravitational assists use the concept of escape velocity to alter spacecraft trajectories.
104. Atmospheric drag complicates achieving escape velocity for surface-launched vehicles.
105. Escape velocity is a threshold; exceeding it ensures a trajectory that escapes the gravitational pull.
106. Re-entry speed calculations are based on reverse considerations of escape velocity.
107. Escape velocity is used in astrophysics to study stellar evolution and supernovae.
108. The energy required to escape depends on the gravitational potential difference.
109. Space elevators could reduce the energy needed to overcome escape velocity.
110. Celestial mechanics relies on escape velocity to predict comet trajectories.
111. The concept of escape velocity applies universally to all gravitational systems.
112. Orbital velocity is related but distinct; it is the speed needed to maintain orbit.
113. Escape velocity can be generalized for rotating or irregularly shaped bodies.
114. Escape velocity principles are applied in artificial gravity design.
115. Gravitational well depth determines escape velocity requirements.
116. Low Earth orbit speeds are typically 7.8 km/s, below escape velocity.
117. Escape velocity calculations assume no external forces, e.g., from other planets.
118. Multi-body systems complicate escape trajectory predictions.
119. Escape velocity informs the design of planetary defense systems.
120. Gravitational slingshots leverage escape velocity for interplanetary travel efficiency.

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