Gravitational Potential Energy, Kinetic Energy and Delta-V

Why Energy?

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I'm sure some point in our lives we've heard about conservation of energy. Rocketry is no exception! In this case we are talking about the conversion of energy between gravitational potential energy and kinetic energy.When an object has velocity, it has kinetic energy. Kinetic energy is proportional to the square of the velocity. Its equation is (1/2)mv^2. Where m is the mass, and v is the velocity.When an object is within the influence of a gravitational force, it has the "potential" to gain kinetic energy while discarding some of its potential energy. Think of a bowling ball for example. A bowling ball suspended 10 meters above the surface of Earth has potential energy because upon release, its gravitational potential energy will be converted into kinetic energy. It gains speed as gravity accelerates it! For this bowling bowl example, the math is quite easy because the gravitational acceleration at the surface of Earth and 10 meters above has very little difference. For objects in orbit, the concept is still the same, but the math is a different story because remember: gravitational force varies with the distance between two centers of mass, and at high altitudes the difference is notable.Having said all this, when a satellite is at its apoapsis, it is farther away from the object it is orbiting and thus, has more gravitational potential energy. On the contrary, when the satellite is at its periapsis, it is closer to the object it is orbiting and has less gravitational energy. Since energy is conserved, where there is less gravitational potential energy should be more kinetic energy and where there is more gravitational potential energy should be less kinetic energy. This is why satellites move faster at their periapsis than at their apoapsis!*This phenomenon can also be explained through Kepler's laws, if you're interested, look it up!Delta means change, V means velocity. If a rocket with a Delta-V of 6000m/s is situated in space, far away from any gravitational influence, it can gain 6000m/s of velocity. Delta-V is a good measurement of what a rocket is capable of as it shows how much it can travel. However, the value of Delta-V does not necessarily mean how fast a spacecraft will be going when it arrives at its destination. If we travel to low earth orbit, we need a Delta-V of 9400m/s, but when we are in Earth Orbit, our velocity is not 9400m/s, it is less. What happened? Some of the kinetic energy is stored as gravitational potential energy(The vehicle loses speed as it flies upwards due to gravity, but it can also regain that speed by falling back into Earth!). Thus, energy is conserved! The Delta-V of a rocket is calculated as the sum of how much velocity each stage can gain.Here is a map of how much Delta-V is required to travel from one place to the other in the solar system.Additionally, here is a Delta-V map for the Kerbol system: