**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.