A satellite is an object in space that orbits or circles around a bigger object. There are two kinds of satellites: natural (such as the moon orbiting the Earth) or artificial (such as the International Space Station orbiting the Earth).

Kepler's laws of planetary motion can be stated as thus;

1. Kepler's First Law (Law of Ellipses):

   Each planet's orbit around the Sun in an ellipse with the Sun at one of the two foci.

2. Kepler's Second Law (Law of Equal Areas):

   A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means a planet moves faster when it is closer to the Sun and slower when it is farther away.

3. Kepler's Third Law (Law of Harmonies):

   The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Mathematically expressed as: T² ∝ a³, where T is the orbital period and a is the semi-major axis of the orbit.

These three laws, formulated by Johannes Kepler in the early 17th century, laid the foundation for our understanding of planetary motion and were crucial in the development of classical celestial mechanics.

Escape velocity is a fundamental concept in physics and astronomy. It refers to the minimum speed an object must achieve to break free from the gravitational pull of a celestial body, such as a planet or a moon. The escape velocity depends on the mass and radius of the celestial body and is calculated using the formula:
v = √(2GM/r)
where G is the gravitational constant,
M is the mass of the celestial body, and
r is its radius. If an object attains or exceeds the escape velocity, it can venture into space without falling back to the surface. For example, Earth's escape velocity is approximately 11.2 kilometers per second (about 25,000 miles per hour).

1. Calculate the gravitational force between two objects with masses of 80 kg and 100 kg, separated by a distance of 6m
2. A rocket is launched vertically from the surface of Mars with an initial velocity of 50 m/s. Calculate the maximum height it will reach. (Acceleration due to gravity on Mars = 3.71 m/s²)
3. Explain how Newton's Law of Universal Gravitation explains the motion of planets around the Sun.
4. Two spheres of masses 5kg and 10kg are 0.3m apart. Calculate the force of attraction between them
5. A force of 200N acts between two objects at a certain distance apart. The value of the force when the distance is halved is ?
6. The force of attraction between two point masses of 10-⁴N when the distance between them is 0.18m. If the distance is reduced to 0.06m, calculate the force
7. A small object with a mass of 2 kg is placed at a point where the gravitational field strength is 15 N/kg. Calculate the gravitational force acting on the object.
8. Determine the escape velocity of Jupiter if its radius is 7149 Km and mass is 1.898 × 10²⁷Kg
9. Determine the escape velocity of the moon if its Mass is 7.35 × 1022 Kg and the radius is 1.5 × 10⁶m
10. The relation between escape velocity (Ve) and orbital velocity (Vo) on the surface of the earth is
11. What would be the escape velocity (in km/s) from a planet of mass 1/4th of mass of earth and radius 1/9 th the radius of earth, if escape velocity from earth is 11 km/s?
12. What would be the acceleration due to gravity (in m/s2) of a planet of radius 6000 km, if escape velocity from it is 12 km/s?
13. Find the gravitational potential energy of 2.5 kg mass kept at a height of 15 m above the ground. The force of gravity on mass 1 kg is 10 N.
14. Calculate the gravitational field intensity if the mass and force of a substance are given as 6 kg and 36 N, respectively
15. If the gravitational force and mass of a substance are 10 N and 5 kg, determine the gravitational field strength.
16. Calculate the escape velocity for a rocket fired from the earth's surface at a point where the acceleration due to gravity is 10m/s² and the radius of the earth is 6 x 10⁶m.
17. Derive the relation between acceleration due to gravity (g) and the gravitational constant (G)