1. What is the Universal Law of Gravitation?
Answer: The Universal Law of Gravitation states that every particle of matter in the universe attracts every other particle 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.
2. How is acceleration due to gravity defined?
Answer: Acceleration due to gravity (g) is the acceleration experienced by an object due to the gravitational pull of the Earth. It has an approximate value of 9.8 m/s² at the surface of the Earth.
3. How does the acceleration due to gravity vary with altitude?
Answer: As altitude increases, the acceleration due to gravity decreases because the distance from the center of the Earth increases, reducing the gravitational force according to the inverse-square law.
4. How does the acceleration due to gravity vary with depth?
Answer: As depth increases inside the Earth, the acceleration due to gravity decreases because a smaller effective mass of the Earth contributes to the gravitational force at that depth.
5. What is Kepler’s First Law of Planetary Motion?
Answer: Kepler’s First Law, also known as the Law of Ellipses, states that the orbit of a planet around the sun is an ellipse with the sun at one of the two foci.
6. What is Kepler’s Second Law of Planetary Motion?
Answer: Kepler’s Second Law, or the Law of Equal Areas, states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
7. What is Kepler’s Third Law of Planetary Motion?
Answer: Kepler’s Third Law, or the Law of Harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
8. Define gravitational potential energy.
Answer: Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. It is given by the formula U = -G * (m₁ * m₂) / r, where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between the centers of the two masses.
9. What is gravitational potential?
Answer: Gravitational potential at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It is a scalar quantity and is given by V = -G * M / r, where M is the mass creating the field and r is the distance from the mass.
10. What is escape velocity?
Answer: Escape velocity is the minimum velocity an object must have to break free from the gravitational attraction of a celestial body without further propulsion. It is given by vₑ = √(2GM/R), where G is the gravitational constant, M is the mass of the celestial body, and R is its radius.
11. Define the motion of a satellite.
Answer: The motion of a satellite refers to its movement around a larger body due to gravitational attraction. This motion is typically elliptical or circular, depending on the velocity and position of the satellite.
12. What is orbital velocity?
Answer: Orbital velocity is the minimum velocity a satellite must have to maintain a stable orbit around a celestial body. It is given by vₒ = √(GM/R), where G is the gravitational constant, M is the mass of the celestial body, and R is the distance from the center of the celestial body to the satellite.
13. How is the time period of a satellite defined?
Answer: The time period of a satellite is the time it takes to complete one full orbit around a celestial body. For a circular orbit, it is given by T = 2π√(R³/GM), where R is the orbital radius, G is the gravitational constant, and M is the mass of the celestial body.
14. What is the total energy of a satellite in orbit?
Answer: The total energy of a satellite in orbit is the sum of its kinetic and potential energies. For a circular orbit, it is given by E = -GMm/2R, where M is the mass of the celestial body, m is the mass of the satellite, R is the orbital radius, and G is the gravitational constant.
15. Explain the significance of the gravitational constant (G).
Answer: The gravitational constant (G) is a fundamental constant that appears in the law of universal gravitation. It quantifies the strength of the gravitational force between two masses. Its value is approximately 6.674 × 10⁻¹¹ N(m/kg)².
16. How does Kepler’s Third Law help in determining the mass of a celestial body?
Answer: Kepler’s Third Law can be used to determine the mass of a celestial body by measuring the orbital period and the semi-major axis of an orbiting object. The mass can be calculated using the formula M = 4π²a³/GT², where a is the semi-major axis, T is the orbital period, and G is the gravitational constant.
17. What factors affect the escape velocity from a celestial body?
Answer: Escape velocity depends on the mass (M) and radius (R) of the celestial body. It increases with greater mass and decreases with larger radius, following the formula vₑ = √(2GM/R).
18. What is the relationship between gravitational potential energy and distance in a gravitational field?
Answer: Gravitational potential energy (U) is inversely proportional to the distance (r) from the center of the mass creating the gravitational field, given by U = -G(m₁m₂/r).
19. How does a satellite’s velocity relate to its orbital radius?
Answer: A satellite’s orbital velocity (vₒ) is inversely proportional to the square root of its orbital radius (R), given by vₒ = √(GM/R). As the orbital radius increases, the orbital velocity decreases.
20. What is meant by geostationary orbit?
Answer: A geostationary orbit is an orbit in which a satellite moves with the same rotational period as the Earth, appearing stationary relative to a fixed point on the Earth’s surface. This orbit has an altitude of approximately 35,786 kilometers above the equator.