When a satellite orbits a planet, the gravitational attraction between the satellite and the planet provides the centripetal force required to keep the satellite in orbit.

Example 1:

• Imagine a tennis ball tied to a string and you're swinging it around your head in a circle. The tension in the string is what keeps the tennis ball moving in a circle. In the case of a satellite, it's the planet's gravity that acts like the string.

• The orbital speed of a satellite depends on its distance from the center of the planet (radius of the orbit) and the planet's mass.

• Orbital speed formula: vorbital = √(GME/r), where G is the gravitational constant, ME is the mass of the Earth, and r is the radius of the orbit.

Example 2:

• The International Space Station (ISS) orbits Earth at an average altitude of around 420 km. Given Earth's radius of approximately 6,371 km, the orbital radius is 6,371 km + 420 km = 6,791 km. Using the orbital speed formula, the ISS's speed is calculated to be around 7.66 km/s.

• A satellite's orbital energy is composed of its kinetic energy (due to its orbital speed) and its gravitational potential energy (due to its distance from the planet).

• Mechanical energy formula: E = -GMm/(2r), where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the radius of the orbit.

Example 3:

• The Hubble Space Telescope (HST) orbits Earth at an altitude of approximately 547 km. Its mass is about 11,110 kg. Using the orbital energy formula, we can calculate HST's mechanical energy in its orbit.