The Only Video Needed to Understand Orbital Mechanics

Summary

This video explores the fundamentals of orbital mechanics, explaining why spacecraft must achieve specific velocities and altitudes to maintain orbit. It covers the concepts of kinetic and potential energy, orbital shapes, and maneuvers like prograde, retrograde, and radial burns. Using real-life examples, such as the SpaceX Dragon capsule's rendezvous with the ISS, the video explains how speeding up or slowing down affects a spacecraft's orbit. Viewers learn how manipulating energy and velocity allows for precise navigation in space, and the video emphasizes the counterintuitive nature of orbital mechanics.

Takeaways

• 🚀 Orbits depend on velocity and altitude; high enough horizontal velocity prevents a spacecraft from falling back to Earth.
• 🌍 Rockets need to reach a certain altitude to avoid air resistance and achieve the speed necessary for orbit.
• ⚡ Mechanical energy is the sum of kinetic energy (speed) and potential energy (altitude). Both are key to understanding orbital motion.
• 🎢 Mechanical energy in orbits works like a roller coaster: kinetic energy and potential energy constantly exchange but the total remains the same.
• 🔄 Orbits are usually elliptical, with the closest point called perigee and the farthest point called apogee when orbiting Earth.
• 🔥 Prograde burns (firing engines in the direction of motion) increase velocity and altitude, making the orbit more elliptical.
• ⏪ Retrograde burns (firing in the opposite direction) reduce velocity and lower the altitude on the opposite side of the orbit.
• 📉 Radial burns (firing engines towards or away from Earth) don’t increase velocity but rotate the orbit without significant energy gain.
• 📐 Normal and anti-normal burns change the inclination of the orbit, but are fuel-intensive and used for orbital corrections.
• 🛰️ When trying to rendezvous with the ISS, a retrograde burn is often used to lower altitude and speed up, then a prograde burn is used to circularize the orbit.

Q & A

What is the basic requirement for a spacecraft to stay in orbit?

A spacecraft needs to achieve sufficient horizontal velocity at a high altitude to stay in orbit. This velocity must counteract the pull of Earth's gravity, allowing the spacecraft to continuously 'fall' around Earth without hitting the surface.

How do kinetic and potential energy contribute to a spacecraft's mechanical energy?

Mechanical energy is the sum of a spacecraft's kinetic energy (due to its speed) and potential energy (due to its altitude). These two types of energy define its overall mechanical energy in orbit.

Why is air resistance absent in orbit, and why is this important?

Air resistance is absent in orbit because spacecraft operate at high altitudes where Earth's atmosphere is extremely thin or nonexistent. Without air resistance, spacecraft can maintain the high speeds necessary for orbit without being slowed down.

How does a spacecraft's orbit change when performing a prograde burn?

A prograde burn increases a spacecraft's velocity and kinetic energy. This causes the spacecraft to gradually climb to a higher altitude, resulting in an elliptical orbit with a larger apoapsis.

What effect does a retrograde burn have on a spacecraft's orbit?

A retrograde burn decreases a spacecraft's velocity, reducing its kinetic energy. This causes the spacecraft to move closer to Earth on the opposite side of the orbit, lowering the orbit's altitude and making it more elliptical.

Why can't a radial-out burn directly increase the altitude of a spacecraft's orbit?

A radial-out burn, which points directly away from Earth, does not add horizontal velocity to the orbit. While it can momentarily increase altitude, the spacecraft slows down as a result, causing the opposite side of the orbit to move closer to Earth, effectively rotating the orbit without substantial energy gain.

What is the difference between a normal burn and an anti-normal burn?

A normal burn changes the inclination of an orbit, causing the spacecraft to rise perpendicular to its current path. An anti-normal burn has the opposite effect, lowering the inclination. These burns rotate the orbit relative to the planet and are fuel-intensive.

What happens to a spacecraft's orbit after a retrograde burn during a rendezvous with another spacecraft?

During a rendezvous, a retrograde burn decreases the spacecraft's velocity, causing it to descend to a lower orbit and move faster relative to the other spacecraft, helping to close the gap between them.

Why does increasing altitude result in a slower orbital speed?

As a spacecraft climbs to a higher altitude, its potential energy increases while its kinetic energy decreases. The trade-off between the two means the spacecraft moves slower in a higher orbit due to the conservation of mechanical energy.

How does the moon's orbit illustrate the relationship between orbital altitude and speed?

The moon, which orbits Earth at a high altitude, moves much slower than satellites in lower orbits. It takes roughly one month to complete one orbit around Earth due to its higher altitude and the corresponding slower orbital speed.

Outlines

00:00

🌍 Understanding Orbital Motion and Energy

The video begins by explaining how orbital mechanics defy our expectations of motion and provides an introduction to the basic concepts required to understand how orbits work. It outlines the importance of being in orbit to remain in space and introduces mechanical energy, which consists of kinetic and potential energy. By giving a spacecraft horizontal velocity, it avoids being pulled back to Earth by gravity, achieving an orbit. The segment also emphasizes the need for altitude to avoid atmospheric resistance and introduces the concept of mechanical energy in relation to kinetic and potential energy.

05:02

🎢 Energy Exchange in Orbits and Elliptical Paths

This section explains how kinetic and potential energy constantly exchange during motion in an orbit. Using a roller coaster as an analogy, it shows how rising away from Earth decreases kinetic energy while increasing gravitational potential energy, and vice versa. A perfectly circular orbit maintains constant energy, but most orbits are elliptical, with two critical points: the closest (perigee) and the farthest (apogee) distances from Earth. The video introduces these terms and touches on the complexity of manipulating orbits in terms of size, shape, and angle.

🚀 Prograde and Retrograde Burns Explained

This part explains the two most common orbital maneuvers: prograde and retrograde burns. A prograde burn, where engines are fired in the direction of motion, increases velocity but not altitude immediately. Over time, it leads to an elliptical orbit as the spacecraft moves farther from Earth. The opposite maneuver, a retrograde burn, decreases kinetic energy and brings the spacecraft closer to Earth. Both burns are key in controlling altitude and orbital shape, manipulating how a spacecraft behaves within its orbit.

🔄 Radial Burns and Their Effects on Orbit

The focus here is on radial burns, another type of orbital maneuver. A radial out burn is done by firing the engines away from Earth, which temporarily resists gravity and alters the orbit, but causes the spacecraft to slow down. This results in the opposite side of the orbit moving closer to Earth. A radial in burn, where engines fire towards Earth, has a similar effect but in reverse. These burns rotate the orbit without significantly changing the spacecraft's energy levels, emphasizing their limited practical use in altering orbits.

📐 Inclination Changes with Normal Burns

The video discusses normal and anti-normal burns, maneuvers that are perpendicular to the direction of motion and used to change the inclination of an orbit. These burns are fuel-intensive and primarily used for fine-tuning the alignment of orbits, such as when matching the orbit of another spacecraft. Inclination changes are critical when aligning with specific targets, and the video emphasizes their cost in terms of fuel consumption.

🛰 Navigating Orbits with Real-life Examples

The final section applies the learned concepts to a real-world scenario: a SpaceX Dragon capsule rendezvousing with the ISS. The video explains how prograde and retrograde burns affect the spacecraft's orbital altitude and speed relative to the ISS. By firing engines in different directions, the spacecraft adjusts its orbit to align with the ISS, demonstrating how these burns are used in practical space navigation. The video concludes with the importance of circularizing the orbit to match the ISS’s orbit, closing with an invitation to subscribe.

Keywords

💡Orbit

An orbit is the curved path of a spacecraft or object around a planet or star, maintained by a balance of gravitational pull and the object's velocity. In the video, the concept of orbit is central to understanding how spacecraft like the SpaceX Crew Dragon capsule stay in space. The script explains how achieving the correct velocity and altitude results in maintaining an orbit around Earth.

💡Kinetic Energy

Kinetic energy is the energy an object has due to its motion. In the video, the spacecraft's kinetic energy is a key factor in its orbit. For example, firing the spacecraft's engines in a prograde burn increases its velocity, thereby increasing kinetic energy, which affects the orbit's shape and altitude.

💡Potential Energy

Potential energy in this context refers to the energy an object has due to its position relative to a gravitational body, such as Earth. The higher the spacecraft’s altitude, the greater its potential energy. The video explains that mechanical energy in an orbit is a sum of both kinetic and potential energy, and these energies are constantly exchanged as the spacecraft moves.

💡Prograde Burn

A prograde burn is when a spacecraft fires its engines in the direction of its motion, increasing its speed. This is crucial in orbital mechanics, as explained in the video. By increasing the spacecraft's velocity, the prograde burn raises the spacecraft's altitude and transforms its orbit from circular to elliptical.

💡Retrograde Burn

A retrograde burn is the opposite of a prograde burn, where the spacecraft fires its engines opposite to the direction of motion, reducing speed. The video demonstrates how this decreases the spacecraft’s kinetic energy and pulls the spacecraft into a lower orbit, closer to Earth.

💡Elliptical Orbit

An elliptical orbit is a non-circular orbit where the distance between the spacecraft and the Earth varies. The video discusses how most orbits are elliptical and how orbital maneuvers like prograde and retrograde burns affect the shape of the orbit. The highest and lowest points in such orbits are known as apogee and perigee.

💡Apoapsis/Apogee

The apoapsis (or apogee in the case of Earth) is the farthest point of an orbit from the central body (Earth). The video explains that after a prograde burn, the spacecraft's orbit becomes elliptical, and the apogee is the point where the spacecraft is farthest from Earth, due to increased potential energy and reduced speed.

💡Periapsis/Perigee

The periapsis (or perigee in Earth’s case) is the closest point of an orbit to the central body. The video discusses how orbital maneuvers like retrograde burns can reduce the spacecraft’s kinetic energy, lowering its perigee and bringing it closer to Earth.

💡Mechanical Energy

Mechanical energy in the context of orbital mechanics refers to the total energy of a system, comprising both kinetic and potential energy. The video explains how mechanical energy remains constant in a closed system, but the spacecraft constantly exchanges kinetic and potential energy as it moves through its orbit.

💡Inclination Change

An inclination change is a maneuver that adjusts the tilt or angle of a spacecraft’s orbit relative to the equator. The video mentions this as a fuel-costly maneuver typically used when a spacecraft needs to match another object's orbit, such as when the SpaceX Dragon capsule aligns its orbit to rendezvous with the ISS.

Highlights

Orbital mechanics can defy normal expectations of motion, requiring a deeper understanding of how objects move in space.

To stay in orbit, a spacecraft needs to achieve a balance between horizontal velocity and the pull of gravity.

High velocities required for orbit can only be achieved in the absence of air resistance, hence the need for high altitude.

Mechanical energy is the sum of kinetic and potential energy in a spacecraft, dependent on its speed and altitude.

A roller coaster is a good analogy for mechanical energy exchange between kinetic and potential energy.

Orbits are generally elliptical, with periapsis (closest point) and apoapsis (furthest point) affecting energy distribution.

Prograde and retrograde burns are common maneuvers to change a spacecraft's orbit, with prograde increasing velocity and retrograde decreasing it.

A prograde burn increases kinetic energy and altitude, making the orbit more elliptical.

A retrograde burn decreases kinetic energy, lowering the spacecraft's altitude on the opposite side of the orbit.

Radial out burns resist gravity but don't provide substantial energy gain, only causing the orbit to rotate.

Normal and anti-normal burns adjust the spacecraft's inclination, rotating its orbit and altering its angle of motion.

Spacecraft rendezvous with the ISS involves intricate orbit matching, using burns to adjust speed and position.

Speeding up a spacecraft can cause it to move into a higher orbit, but paradoxically slow down its orbital velocity.

Slowing down a spacecraft can bring it into a lower orbit, allowing it to approach a faster-moving object like the ISS.

Final orbital maneuvers require circularization to match the target's orbit and complete the rendezvous.

Transcripts

[Music]

orbital mechanics can defy our normal

expectations of motion

and in this animation we'll see how

but to understand how let's first review

a few things

why we need to go into an orbit to stay

in space

what mechanical energy is and we'll also

learn all about orbital Maneuvers we

will then look at why when navigating in

an orbit we need to slow down our

spacecraft to move faster and speed up

to go slower

first of all what makes up an orbit is

it just how far we are from Earth's

surface well if we place the SpaceX crew

Dragon capsule hundreds of kilometers

above Earth with no velocity gravity

represented by the blue arrow will pull

on it and will follow the trajectory of

this blue line and fall out of the sky

towards Earth but if we give it some

horizontal velocity represented by the

red arrow the trajectory begins to

change and if you move fast enough

horizontally the spacecraft will never

hit Earth

these high velocities that are required

to achieve orbit can only be

accomplished with the absence of air

resistance so therefore the rocket has

to have a high enough altitude to be out

of the dense atmosphere

this speed and altitude of the

spacecraft gives the spacecraft kinetic

and potential energy

kinetic energy from how fast it's going

and potential energy from how high it is

or its altitude

these two forms of energy added together

make up mechanical energy and can be

calculated through this formula

a great illustration of mechanical

energy is a roller coaster

a roller coaster train will have

constant mechanical energy but will

continually exchange kinetic energy for

potential energy and vice versa

depending on where it is on the track

as it rises away from Earth it slows

down lowering its kinetic energy but

increasing its gravitational potential

energy

and as it falls to Earth the opposite is

true

a perfectly circular orbit will have a

constant kinetic and potential energy

throughout each orbital period if the

orbiting altitude is constant

but orbits are never perfectly circular

meaning they are elliptic

in elliptical orbit will have a point

that is closest to its orbiting body

which is referred to as the periopsis

and a point where the orbital height is

the furthest from its orbiting body

which is referred to as the apoapsis

when talking about a spacecraft orbiting

Earth these two points are referred to

as the perigee and apogee

manipulating the size shape and angle of

your orbit makes up a large portion of

understanding orbital mechanics

let's briefly review different ways of

manipulating orbits to ultimately

understand why we need to slow down our

spacecraft to go faster and speed up to

go slower

the most common Burns that are used are

the pro-grade and retrograde Burns

pro-grid and retrograde burns are Burns

whose burn vectors are parallel with the

direction of motion let's look at a

specific example of each first the

prograde burn the prograde burn is when

you fire your engines into the direction

you came from a pro-grade burn will

increase your velocity or kinetic energy

at that specific point but not your

altitude or potential energy

but as you continue in your orbit with

higher kinetic energy your inertia will

cause your outward centrifugal force to

be higher than that of gravity resulting

in you to slowly fall further and

further from Earth as you climb in

altitude

your orbit will now be elliptic and look

like this

now let's look at that again

you're added inertia and centrifugal

force is now a little stronger than

before and this causes you to resist

gravity a little more resulting in you

to fall away from Earth

[Music]

if we were to fire our engines in the

exact opposite direction this would be a

retrograde burn and it is very similar

to a pro-grade burn but in the exact

opposite direction

it therefore subtracts kinetic energy

from the orbit at that point of where

you fired your engines and this will

affect the altitude of the opposite side

of your orbit bringing it closer to

Earth

now if you want to increase your Orbit's

altitude can't you just fire your

engines at Earth instead of a pro-grid

burn

well let's do it and see what happens

this burn is known as a radial out burn

a radial out burn will result in your

spacecraft to resist the effects of

gravity to an extent

maintaining a more straight trajectory

throughout the burn but because there's

no velocity added to your orbit as you

raise your altitude from Earth you slow

down this will pull the opposite side of

your orbit towards Earth

the result is that your orbit rotates

about your spacecraft with no

substantial energy gain

a radial inburn where you fire your

Rockets towards space will have the same

effect but in Reverse like this

the last types of burns that can be made

are the normal and anti-normal burns the

normal anti-normal burns are

perpendicular to your direction of

motion as you complete a normal burn

your rocket begins to rise up away from

your initial orbit but because you are

still orbiting the planet your orbit

will slowly rotate with the center of

rotation being the planet you orbit

this change in orbit is referred to as

an inclination change and is a rather

fuel costly maneuver

they are generally only used for

Corrections when matching the orbit of

another spacecraft

now that we've reviewed the basics of

orbital mechanics let's use what we

learned to try to navigate in an orbit

let's look at a real life example a

SpaceX Dragon capsule rendezvousing with

the ISS

say you're in the same orbital path as

the ISS with it just in front of you

intuitively we'll fire our Rockets

behind us to go closer to it a pro-grade

burn

let's see how this affects your orbit

relative to the ISS

this increased kinetic energy will begin

to increase the outward centrifugal

force pulling the spacecraft away from

Earth faster than Earth gravity can pull

back on it

this in return causes the rocket to gain

altitude or potential energy and

therefore lose kinetic energy

much like a roller coaster on the

incline part of a track

this gain and potential energy results

in the spacecraft to lose kinetic energy

our new orbit now has a higher altitude

and therefore a slower average speed

the moon's orbit is a great example of

this higher and slower orbit as it takes

a month to orbit the Earth

if we follow the position of our

spacecraft relative to the ISS it will

rise up above the ISS and fall further

behind as a result of this longer

orbital period

well what if we do just the opposite

let's try firing our Rockets into the

direction we are heading a retrograde

burn slowing us down to see what happens

if we fire our rockets in this direction

we'll decrease our kinetic energy at

that point and our potential energy

Remains the Same

but as we continue to orbit the

decreasing kinetic energy will result in

the spacecraft being pulled to Earth

faster than our inertia pulls it away

this will cause an exchange of energy

from potential to kinetic energy

now if we follow the path of the orbit

relative to the ISS we will begin to

approach it as we pass under it

this only leaves us with one problem we

are only at the correct orbit as the ISS

at one point our apoapsis a last progrid

burn is required to now circularize the

orbit to replicate the orbit of the ISS

thanks for watching and please consider

subscribing