@@MBKill3rCat I haven’t even finished school yet... normally, I just listen to what he says twice and try to express it in my own words, in my head obviously. That’s how I get through school too, works!
Dad: "Son you need to get smarter to better your future." Me: "Meh" Mother: "You need to get smarter so you can get a good wife." Me: "Meh" Scott Manley: "Here's how you calculate the........" Me: "I must get smarter so I can understand what he's talking about!"
My math teacher can keep my interest in 70 minutes he gave me this homework:Research the following for a space rocket of your choice. Dry mass (excl payload and fuel) and max fuel capacity Thrust and fuel consumption of engine Calculate the max payload mass that the rocket can accelerate to escape velocity. This question is hard. Your goal is to develop strategies for breaking the question down into smaller pieces, identifying what assumptions you need to make for missing information, finding shortcuts and approximations, and figuring out what mathematical methods and tools are required. A full solution requires integral calculus. Start by working out a solution using discrete time periods. And I only go in 7th grade
You have no idea how happy this made me. Someone is finally able to teach the basics of orbital mechanics using a videogame as an example. Honestly this could maybe end up being a whole new way to educate.
I cannot tell you in words how much I enjoyed this video. So many practical applications! My head is going to explode, not from confusion, but from joy! As Тимур Юлдашев said, MOAR!
OMG Scott Manley is the best! This is exactly the video I needed to help with my NASA scholarship program. The reading did an ok job of explaining it but this really hit it home. I cant wait for the next video!
Scott Manley I wanted to thank you for your video "Orbital Mechanics on paper" Your video helped my friend and I (Mostly him) build a calculator that accurately calculates the velocity and deltaV requirements for the altitude you desire. We will be uploading the calculator with instructions for use on the reddit for KSP when it is ready. When used correctly The excel will be able to calculate both velocity and delta V for all of the planets and moons in KSP as of this date. We hope to help others create rudimentary flight plans like we have been! This was super exciting for us because we discovered that the KSP wiki has incorrect escape velocities for at least Kerbin. We will keep you posted when we release the calculator if your interested! Again thank you so so much for your videos and all of your contributions to KSP, UA-cam, education and science!
Finally understanding the math that puts my spacecraft in orbit. Thank you, Scott! As a side note, everybody who plays KSP can apply this stuff pretty much instinctively. That's pretty awesome.
Catching your mistake and correcting it in the video was classy, man. I've had to do that many a time myself, and in papers being submitted for peer review, too. Well done.
The best part of this video is the slight echo in the sound. It makes me feel like I'm back in a college lecture hall. Also, this isn't so bad because I already made myself learn this stuff to fly properly in KSP, back in VERY early versions - when there wasn't Kerbal Engineer, weren't orbital calculators, certainly weren't any maneuver nodes! So it was either: calculate your transfer orbits by hand, or guess and probably screw up so epically that not even Jeb could save you.
He took the radius of Earth (around 6,371 kilometers) and added the 300 kilometers we are positioning our satellite above Earth. Then, he converted kilometers to meters by multiplying by 1,000. That gives you, in scientific notation, 6.67 × 10^6.
Right…thanks for the clarification at the end. I was a bit confused yesterday but honestly too tired (~1am) to bother responding. And I can only add the same comment as I did yesterday again which would be PLEASE MAKE MORE OF THESE. Very informative, you're a great teacher.
OF course this stuff is easy I'm doing nat 5 physics and mathematics next year and I'm in 3rd year of high school and I understand a lot of this Also I'm in a Scottish school
Ksp has taught me so much about orbital mechanics(And you too scott). All those Discovery channel shows finally made sense and I because space jesus. Thank you.
Hey Scott, this is incredible! KSP has so much potential bringing awareness to orbital mechanics and in general, physics. You're one of those players who genuinely gets into the quantitative details instead of just sticking to some loose jargons like "delta-V" or "momentum" without explanation. As a graduate student in Astronomy, I really appreciate this. Applause all the way from Hong Kong :-) It'd be nice if you also mention that the velocity equation is a direct result of the conservation of energy (KE vs gravitational PE). Also, another very useful thing is Kepler's 3rd Law (that a^3 is directly proportional to period^2). This brings me to a suggestion on a sequel to your video "How To Setup A Geostationary Communications Network": - how to achieve an orbit of a period of 4 hours (or any desired time) without readouts from mods such as Flight Engineer / MechJeb, provided we know that we need a = 3468.75 km for a 6-hour orbit - how to setup the periapsis (periKee?) of this 4-hour orbit with its apoapsis at the altitude 2868.75 km - why can't we use a 2-hour orbit for the transfer - for a 6-satellite configuration (like that shown on the wiki page "Tutorial:Satellite Coverage"), (similarly) can we use an 1-hour transfer orbit? Why or why not? - If not, what period can we use? Speaking of plane changes, I'd love to find out how different the fuel usage will be when changing from an equatorial orbit to a polar one by (1) directly burning (anti-)normal while staying in a low-Kerbin orbit or (2) gravity assist from the Mun.
Was confused about the second error, guessed i had missed something, it seems i didn't! I think this is a good lesson to everyone, to keep your eye on the ball even while listening to Scott!
I liked this a lot. Hope to see many more videos like this. I know it would be a massive pain, but one way that I can think of that might improve this is if you could pair examples up with visuals from the game. I can handle equations pretty well, but being able to visualize every step of a problem is a huge help to understanding something intuitively, instead of just plugging in numbers for a rote calculation.
Thank You Scott, I'm a high school drop out, I have mental health issues that stopped me from being able to attend public education, but I have an IQ of 135. I always struggled with math subjects growing up, but your videos are the mix of immense mathematical education, in a fun and humorous way and I find your methods of teaching perfect for me needs as I'd love to learn everything I can on orbital mechanics and astrophysics in general. I already have a good grasp of it!
One thing that has always helped me wrap my head around some of this is thinking about how kinetic energy and gravitational potential energy flow back and forth into each other as the object travels in the elipse. At apoapsis when the velocity and kinetic energy is lowest, the remainder of the energy is "stored" as potential energy, and at periapsis, all of that potential energy has been converted to kinetic. K+P is constant at any point in the orbit.
Deriving v^2 = GM/r Centripetal Force = (v^2 * m)/r Gravitational Force = GMm/r^2 Centripetal force is the gravitational force Therefore mv^2/r = GMm/r^2 Goes to v^2=GM/r
Amazing! Thank you! The part where you make a slight error feels very reminiscent of, like, every class I take. The students: “professor you made a slight calculation error!” Professor: “Um actually in the part ur specifying, I did not. But the error the entire class FAILED to recognize was this one here!” Students: *feel dumb*
Just a comment, Scott ... you're "Like" to "Dislike" statistics are pretty astounding ... not sure what this means in a social context - and, I have no idea what your viewership statics might mean financially - but, I think this means - people really like the content you're creating. I know I do.
Hi Scott, I was monitoring the upper stage velocity and altitude on the recent SpaceX SPT-2 mission launch and tried to reproduce these using the orbital mechanics formulas that you presented in this series. The vehicle was launched into a very elliptical orbit and achieved an Apoapse Altitude of 854 km with a velocity of 24,544 km/s (6,817.8 m/s) somewhere over the Indian Ocean just east of the west coast of Australia. In order to recreate these conditions at Apoapse, I had to use a Periapse Altitude of -1,105 km, which is inside the earth. Can you please explain this, or better still, present a further episode of your Orbital Mechanics videos where you take us through this launch
it's videos like this that me question what I can learn from school. here I learn rocket science (kind of), yet in school, i heard something about being able to calculate the sides of a right triangle (trigonometry) but when ask about it, I allways get a response resembling: "you'll learn about it later.. maybe..... eventually". and then I venture to the internet and learn more than they'd ever hint at. you know you failed when you teach slower in the school your working than some random person learns by googling it.
You can acutely do a lot of stuff when you know how to calculate the sides of a triangle like measuring large distances (look up how they calculated the meter), you can measure the distance between the earth and the sun and if you go really crazy you can observe the change of gravitation on earth. Just try to find something that's fun for you to do.
+playerguy2 That's because to get to learn the cool stuff you need to know basic math first. They don't teach much past trigonometry, functions, etc. Because you gotta learn calculus to really start learning the how and the why behind physics.
Liam Mehle triangles are so important, and Pythagorus, it’s literally how we measure the distance between two objects and in building to find right angles
I mostly wanted to learn orbital mechanics, but the physics textbook i've been using covered the three kepler laws and centrifugal force Thank you Scott Manley. I've wanted to plan out my own moon mission ever since I was in high school.
oh thank Jesus Christ you explained G, Wikipedia did an absolutely terrible job at explaining it and it was frustrating and depressing at the same time.
totally mindblown :D i understand formula but cannot imagine counting this by head and paper without using spreadsheet or even calculator. p.s. MechJeb should be updated to MechManley :D
you learn me more here than my 6 years in high school (In the belgian system I don't have any idea of the american system). Thanks it will be really easy to code a little thing who do the math for KSP orbit.
To make it simple, a circle has one central point known as the "focus" where every point equally measured away from the focus forms the circle. In an ellipse, the "focus has shifted so that there is more than one focus. Each "center point" (foci) is no longer the center of a circle and each point of reference is known as the plural of "focus" or "foci". An ellipse has two "foci" and its circumference is measured from points measured from both "foci". It no longer looks like a circle but more like a racetrack. If you took a circle and put a dot in the center, that dot would be the "focus'. If you took that dot and moved it only one atom's distance away and drew a point equidistant from both, no matter how close those two dots were, you would have an ellipse. Once the two dots moved back and merged into one dot, then, and only then would you have a circle. I know, dah.
Thank you so much! You made me remember why I love Trig! I haven't felt that kind of excitement in ages! I feel so stupid. I couldn't understand where you were getting the number for r. I'm so used to seeing r as the radius that it took my brain 30 mins to realize it didn't make since...because I forgot that diameter = 2 x radius. Younger me would be ashamed. ToT
Scott, quick question, is the semi-latus rectum of an orbit the altitude of a spacecraft when the vertical velocity equals the lateral velocity? Also, can you go over bi-elliptic transfer orbits. Also, is the eccentricity of an orbit the apogee altitude divided by the semi-major axis, and then have 1 subtracted from it?
I chose the wrong major in college, I should have went into physics rather than business. After one 13 minute video, I now understand orbital mechanics better than I have ever understood macroeconomics!
The number in question is at 4:42, at 300 km above the Earth's surface with the distance from earth's surface to it's center being 6,371 km should mean that the body in orbit is at 6671 km from the earth's center. Where did that extra 7 km come from?
Thank you, Scott! I am math graduate student but I was too lazy to dive deep into orbital mechanics. Can you tell me where to see the derivation of this v^2 formula from the gravity law? Another small error: 8:53 must be "a becomes your geostationary radius", not "velocity".
for circular orbits F=G*m*M/r² ma=G*m*M/r² a=G*M/r² V²/r=G*M/r² (radial acceleration is V²/r) V²=G*M/r and then adapted to account for eccentricity to V²=G*M*(2/r-1/((r1+r2)/2) the derivation for that is here, derived using conservation of energy (en.wikipedia.org/wiki/Vis-viva_equation)
I think it would be helpful to explain the form of the equation relating altitude to velocity in an elliptical orbit as simply the conservation of total mechanical energy. As the satellite orbits, energy flows back and forth between kinetic (which goes as v^2) and potential (which goes as -GM/r) with a constant sum assuming no drag or perturbations.
202penguin As my understanding of the video has it this equation treats the body that the projectile is orbiting around as a point mass. That means that in a game such as kerbal space program R should indeed be your altitude plus half of kerbins diameter.
Nick Dunn I bought a fridge magnet in the KSC gift shop that originally said What part of GxmxM/R = mxVesc^2 Don't you understand? It's only rocket science! A bunch of us, including some actual NASA rocket scientists, stood looking at this thing trying to figure it out. I realized it was probably designed by some English major who didn't know that you don't write 'x' for multiplication in algebra, and that you can cancel 'm' from both sides. So I corrected it to read GM/R = Vesc^2/2 The left side gives the negative of the specific gravitational potential energy and the right side gives the specific potential energy (in joules/kg). When they're equal, the sum of the potential and kinetic energy is zero and the object has exactly enough velocity to escape.
TVTacon You are indeed right! My bad. What I should have said: the left side, GM/R, is -1 times the specific potential energy, energy per unit mass, due to the planet's gravity (potential energy is either 0 or negative, so the -1 makes it positive). The right side, V^2/2, is the specific *kinetic* energy. When V is escape velocity, they will be equal.
ApolloWasReal Actually, I am a bit confused, I know you can easily find the orbital speed equation for a circular orbit with centripetal force, (mv^2)/r = GMm/r^2, but when you do it using convservation of mechanical energy you get 1/2 * m * v^2 = GMm/r, which gives you v^2 = 2GM/r, which is not just GM/r as it should be. Am I going crazy or something? N.b. you can just say gravitational potential or g instead of specific gravitational potential energy, just abit easier to type haha.
Is it me or the ellipse at the start looks like a grumpy man ? Thank you for the physics lesson, I am a fresh subscriber and I really enjoy all your entertaining and instructing videos :)
I kept hearing "in the next video" so i went to look for it and didn't find it. I was very upset. Then I found out this video was uploaded 4 hours ago. Scott puts out a video more often than I change underwear.
You said geostationary orbit is ~42,000m up... I think you meant km! Great video though, love leaning this stuff, hope you make more like this! I've always enjoyed using first principles to understand things, so the usual way many tutorials say you should do interplanetary transfers is to look up the angles in some calculator / reference or something, which annoys me... I want to understand WHY these angles are needed and HOW they were worked out!
This is great! I love it! But I have a problem here: Given a speed V at an altitude R orbiting a body of mass M, how can I calculate the semi major axis, periapse, and apoapse? I found a way to find the semi major axis: V^2 = GM(2/R-1/A) (as scott shows us) V^2/GM = 2/R-1/A V^2/GM-2/R=-1/A -1/(V^2/GM-2/R)=A I hope this is right, please correct me if it isn't But then how do I calculate the pe and ap?
Scott Manley For the velocity at 5:00, I got 7729 m/s rather than your 7724 m/s. I'm guessing this is because we used different numbers for the radius of the Earth to convert from distance from surface to distance from center of gravity, but I would like to know what number you used. Was it Google's 6371 km, or Wikipedia's 6378.1 km? Or something else? I wasn't able to find the Earth's equatorial sea level radius anywhere...
Every single time you use the word 'simple' in this video, it instantaneously plunges me into the deepest depths of despair.
People who teach things tend to talk down to people for not knowing things, and they tend to not give very good explanaitions.
Rocket science and physics is simple in the same way that opperating a bicycle is intuitive for a giraffe.
Tbh it IS fairly simple
@@valentinaou6579 Maybe if you passed an A-Level in further mathematics.
@@MBKill3rCat I haven’t even finished school yet... normally, I just listen to what he says twice and try to express it in my own words, in my head obviously. That’s how I get through school too, works!
Dad: "Son you need to get smarter to better your future."
Me: "Meh"
Mother: "You need to get smarter so you can get a good wife."
Me: "Meh"
Scott Manley: "Here's how you calculate the........"
Me: "I must get smarter so I can understand what he's talking about!"
*"You need to get smarter so you can get a good wife."*
@@TheGreenTaco999
She meant to say "richer"
🤣
C H I ain’t sayin she a gold digger, but she ain’t messin with no broke niggaz
TheGreenTaco999 Isaac Newton did not go chasing after women because it distracted him from learning math
@@pavlo3511 Isaac Newton was also well known to be a miserable person.
Only Scott can keep my interest with maths for over 13minutes... :)
***** A good starting video is "math" vs. "maths" problematic :D
***** thanks for the tip.
***** Confirming Numberphile is worth watching I even learned a couple of things that I didn't already know.
+Scott Manley yes, but I think this video qualifies as rocket science.
My math teacher can keep my interest in 70 minutes he gave me this homework:Research the following for a space rocket of your choice.
Dry mass (excl payload and fuel) and max fuel capacity
Thrust and fuel consumption of engine
Calculate the max payload mass that the rocket can accelerate to escape velocity.
This question is hard. Your goal is to develop strategies for breaking the question down into smaller pieces, identifying what assumptions you need to make for missing information, finding shortcuts and approximations, and figuring out what mathematical methods and tools are required.
A full solution requires integral calculus. Start by working out a solution using discrete time periods.
And I only go in 7th grade
You have no idea how happy this made me. Someone is finally able to teach the basics of orbital mechanics using a videogame as an example. Honestly this could maybe end up being a whole new way to educate.
You should do more of this. I've been watching your videos in my Physics class and so far have learned more from you than the class itself :P
MrSplodgeySplodge actually my teacher showed it to us, and gave us a quiz. I thought i learned from them too
you explain this much better than my physics teacher
""explain"? what's that?" -my physics teacher.
I guess she isn't Manley enough :)
oh... PS I like the "Fly Safe" motto after correcting a math error that would have killed my Kirbals!!
Teach me your ways, O Manley, that I might bring glory to my Kerbals!
It warms my heart to see physics on UA-cam in a gaming context. Games are such a great tool for bringing science to the fore. Thank you, sir.
Thank you, Scott, for reminding us that space exploration in general and KSP in particular are not only about explosions (controlled or not)!
I cannot tell you in words how much I enjoyed this video. So many practical applications! My head is going to explode, not from confusion, but from joy! As Тимур Юлдашев said, MOAR!
Well done, Scott! You truly are both a gentleman and a scholar :)
Scott! This is amazing, please do more of these educational videos because I find them simply wonderful!
OMG Scott Manley is the best!
This is exactly the video I needed to help with my NASA scholarship program.
The reading did an ok job of explaining it but this really hit it home. I cant wait for the next video!
Scott Manley I wanted to thank you for your video "Orbital Mechanics on paper"
Your video helped my friend and I (Mostly him) build a calculator that accurately calculates the velocity and deltaV requirements for the altitude you desire.
We will be uploading the calculator with instructions for use on the reddit for KSP when it is ready.
When used correctly The excel will be able to calculate both velocity and delta V for all of the planets and moons in KSP as of this date. We hope to help others create rudimentary flight plans like we have been!
This was super exciting for us because we discovered that the KSP wiki has incorrect escape velocities for at least Kerbin. We will keep you posted when we release the calculator if your interested!
Again thank you so so much for your videos and all of your contributions to KSP, UA-cam, education and science!
Finally. I was waiting for videos like these to be uploaded. really helpful.
Finally understanding the math that puts my spacecraft in orbit. Thank you, Scott!
As a side note, everybody who plays KSP can apply this stuff pretty much instinctively.
That's pretty awesome.
I was procrastinating and watching this.
Now my mind is jelly.
You inspire me
Catching your mistake and correcting it in the video was classy, man. I've had to do that many a time myself, and in papers being submitted for peer review, too. Well done.
The best part of this video is the slight echo in the sound. It makes me feel like I'm back in a college lecture hall.
Also, this isn't so bad because I already made myself learn this stuff to fly properly in KSP, back in VERY early versions - when there wasn't Kerbal Engineer, weren't orbital calculators, certainly weren't any maneuver nodes! So it was either: calculate your transfer orbits by hand, or guess and probably screw up so epically that not even Jeb could save you.
Thank goodness for maneuver nodes in ksp
I love it the way it looks so complicated but actually isn't that hard is brilliant
4:41 Where did you get the 6.678 from? I've been trying to work it out all day :/
He took the radius of Earth (around 6,371 kilometers) and added the 300 kilometers we are positioning our satellite above Earth. Then, he converted kilometers to meters by multiplying by 1,000. That gives you, in scientific notation, 6.67 × 10^6.
Yes, but it's still 6.671 * 10**6
Finally someone that really shows the math. Thank you so much!!
Right…thanks for the clarification at the end. I was a bit confused yesterday but honestly too tired (~1am) to bother responding.
And I can only add the same comment as I did yesterday again which would be PLEASE MAKE MORE OF THESE. Very informative, you're a great teacher.
Complex mathematics done with a crayola. Gotta love it
This is far from complex mathematics.
Jakob Schytz Basic Physics (=
Jakob Schytz
well its rocket science and it sounds funnier the way I said it
It is on the tip of the iceberg unfortuanatly
OF course this stuff is easy I'm doing nat 5 physics and mathematics next year and I'm in 3rd year of high school and I understand a lot of this
Also I'm in a Scottish school
Ok, sooo im in middle school and I got challenged to describe the math + how orbital mechanics works and this is a godsend. Thanks soo much Scott!
Ksp has taught me so much about orbital mechanics(And you too scott). All those Discovery channel shows finally made sense and I because space jesus.
Thank you.
This is the best video by far I have seen explaining this topic.
Hey Scott, this is incredible! KSP has so much potential bringing awareness to orbital mechanics and in general, physics. You're one of those players who genuinely gets into the quantitative details instead of just sticking to some loose jargons like "delta-V" or "momentum" without explanation. As a graduate student in Astronomy, I really appreciate this. Applause all the way from Hong Kong :-)
It'd be nice if you also mention that the velocity equation is a direct result of the conservation of energy (KE vs gravitational PE). Also, another very useful thing is Kepler's 3rd Law (that a^3 is directly proportional to period^2).
This brings me to a suggestion on a sequel to your video "How To Setup A Geostationary Communications Network":
- how to achieve an orbit of a period of 4 hours (or any desired time) without readouts from mods such as Flight Engineer / MechJeb, provided we know that we need a = 3468.75 km for a 6-hour orbit
- how to setup the periapsis (periKee?) of this 4-hour orbit with its apoapsis at the altitude 2868.75 km
- why can't we use a 2-hour orbit for the transfer
- for a 6-satellite configuration (like that shown on the wiki page "Tutorial:Satellite Coverage"), (similarly) can we use an 1-hour transfer orbit? Why or why not?
- If not, what period can we use?
Speaking of plane changes, I'd love to find out how different the fuel usage will be when changing from an equatorial orbit to a polar one by (1) directly burning (anti-)normal while staying in a low-Kerbin orbit or (2) gravity assist from the Mun.
Just me or can anyone else nearly smell the pen?
Simply, I want MOAR.
The only game I've ever played that required physics and math class before playing it. I LOVE IT!
Was confused about the second error, guessed i had missed something, it seems i didn't! I think this is a good lesson to everyone, to keep your eye on the ball even while listening to Scott!
I liked this a lot. Hope to see many more videos like this. I know it would be a massive pain, but one way that I can think of that might improve this is if you could pair examples up with visuals from the game.
I can handle equations pretty well, but being able to visualize every step of a problem is a huge help to understanding something intuitively, instead of just plugging in numbers for a rote calculation.
Using a "d" instead of a little triangle for delta bugged me the most scott. Great video keep up the good work!
I understood none of this but enjoyed it completely.
...Maaath! Also learned something new, thanks Scott.
Love this Scott! Keep doing these! It's very helpful/interesting to learn about the math behind the fun in KSP!!
I’ve decided to calculate my transfer orbits in ksp by hand. Figured this was a good place to start. Great video!
This is like Vihart explaining Math :D but orbital mechanics being explained. But still awesome. Thank you Scott!
Thank You Scott, I'm a high school drop out, I have mental health issues that stopped me from being able to attend public education, but I have an IQ of 135. I always struggled with math subjects growing up, but your videos are the mix of immense mathematical education, in a fun and humorous way and I find your methods of teaching perfect for me needs as I'd love to learn everything I can on orbital mechanics and astrophysics in general. I already have a good grasp of it!
get going, brother
Woooosh.
This is the sound this video made as it went over my head.
Love your video's Scott, but you made my head hurt.
You realize in the first 45 seconds you draw a Canadian from South Park right?
+Mark Williams I didn't notice. (Ik I'm not scott)
NASA called, they said you've got the job!
One thing that has always helped me wrap my head around some of this is thinking about how kinetic energy and gravitational potential energy flow back and forth into each other as the object travels in the elipse. At apoapsis when the velocity and kinetic energy is lowest, the remainder of the energy is "stored" as potential energy, and at periapsis, all of that potential energy has been converted to kinetic. K+P is constant at any point in the orbit.
Scott I found this really useful. I've just recently been able to calculate delta v by myself so you really helped me
You are the best math teacher ever!
I wish Scott Manley was my teacher for all my math classes. It'd keep me awake long enough to learn something new.
Deriving v^2 = GM/r
Centripetal Force = (v^2 * m)/r
Gravitational Force = GMm/r^2
Centripetal force is the gravitational force
Therefore
mv^2/r = GMm/r^2
Goes to v^2=GM/r
You should start a whole series on this stuff. You are a great teacher
Thanks so much for this, and I really hope you keep making more.
i dont understand every scientific term you use, but: more of this! It is interesting and educational
Thank you so much Scott! I couldn't find a good tutorial anywhere, and I love the maths!
Wasn't until i took physics that i could understand this, now that i have this very useful, thank you good sir
Keep making these and you might have 207,154 new scientists
Just had my first physics class in college. I watch this video again and now I understand this, yay :)
This all actualy made perfect sense. Nice job!
AWESOME! i have been wanting a 'ksp physics on paper' for so long. Hopefully this series goes on!
Amazing! Thank you!
The part where you make a slight error feels very reminiscent of, like, every class I take.
The students: “professor you made a slight calculation error!”
Professor: “Um actually in the part ur specifying, I did not. But the error the entire class FAILED to recognize was this one here!”
Students: *feel dumb*
Just a comment, Scott ... you're "Like" to "Dislike" statistics are pretty astounding ... not sure what this means in a social context - and, I have no idea what your viewership statics might mean financially - but, I think this means - people really like the content you're creating. I know I do.
Thanks Scott Manley - was stuck on this on an assignment.
You've got one more subscriber (y)
Thanks for this short on orbital mechanics. It was a good refresher for me.
This is great "revision" for my Orbital mechanics exam on Thursday! I can revise and procrastinate at the same time xD
Hi Scott, I was monitoring the upper stage velocity and altitude on the recent SpaceX SPT-2 mission launch and tried to reproduce these using the orbital mechanics formulas that you presented in this series. The vehicle was launched into a very elliptical orbit and achieved an Apoapse Altitude of 854 km with a velocity of 24,544 km/s (6,817.8 m/s) somewhere over the Indian Ocean just east of the west coast of Australia. In order to recreate these conditions at Apoapse, I had to use a Periapse Altitude of -1,105 km, which is inside the earth. Can you please explain this, or better still, present a further episode of your Orbital Mechanics videos where you take us through this launch
Well now it is time to launch a rocket to LEO with great precision. Thank you Scott!!!! You're my hero of the day!
Please make as many of these as possible! loved it. thank you
I was so looking forward to this. Thank you Scott, I really appreciate you passing on your knowledge to the community. Please teach us more of this :)
Thanks for this. Really interesting and engaging to see the math behind it all.
it's videos like this that me question what I can learn from school. here I learn rocket science (kind of), yet in school, i heard something about being able to calculate the sides of a right triangle (trigonometry) but when ask about it, I allways get a response resembling: "you'll learn about it later.. maybe..... eventually". and then I venture to the internet and learn more than they'd ever hint at. you know you failed when you teach slower in the school your working than some random person learns by googling it.
You can acutely do a lot of stuff when you know how to calculate the sides of a triangle like measuring large distances (look up how they calculated the meter), you can measure the distance between the earth and the sun and if you go really crazy you can observe the change of gravitation on earth. Just try to find something that's fun for you to do.
+Ic3Tank thanks but the point is: it's usefull but i stopped short of learning this in school.. not tower atleast.
+playerguy2 That's because to get to learn the cool stuff you need to know basic math first. They don't teach much past trigonometry, functions, etc. Because you gotta learn calculus to really start learning the how and the why behind physics.
Liam Mehle triangles are so important, and Pythagorus, it’s literally how we measure the distance between two objects and in building to find right angles
At 0:35 you appear to have drawn a bemused face haha, I love your science videos Scott! You're an inspiration to me :)
Почему я не увлекался этим в школе .... Так был бы самым умным )) Very interesting )) Thank you!
Scott, I am so damn glad I chose to subscribe to you so long ago.
Thanks, in part, to this series of videos I have actually been able to convert several moon hoaxers over to the side of logic. Thanks, Scott!
Damn, if I had scott manley as a physics teacher in high school, I probably would have gone that way after that...
I mostly wanted to learn orbital mechanics, but the physics textbook i've been using covered the three kepler laws and centrifugal force
Thank you Scott Manley. I've wanted to plan out my own moon mission ever since I was in high school.
oh thank Jesus Christ you explained G, Wikipedia did an absolutely terrible job at explaining it and it was frustrating and depressing at the same time.
Love it!!! i recently did physics with the F = GMm/r^2 this just gave me more info for it :D
Great video! Another succesful blow to the face of ignorance!
I would love to have a spreadsheet for this :)
totally mindblown :D i understand formula but cannot imagine counting this by head and paper without using spreadsheet or even calculator.
p.s. MechJeb should be updated to MechManley :D
you learn me more here than my 6 years in high school (In the belgian system I don't have any idea of the american system). Thanks it will be really easy to code a little thing who do the math for KSP orbit.
To make it simple, a circle has one central point known as the "focus" where every point equally measured away from the focus forms the circle. In an ellipse, the "focus has shifted so that there is more than one focus. Each "center point" (foci) is no longer the center of a circle and each point of reference is known as the plural of "focus" or "foci". An ellipse has two "foci" and its circumference is measured from points measured from both "foci". It no longer looks like a circle but more like a racetrack.
If you took a circle and put a dot in the center, that dot would be the "focus'. If you took that dot and moved it only one atom's distance away and drew a point equidistant from both, no matter how close those two dots were, you would have an ellipse. Once the two dots moved back and merged into one dot, then, and only then would you have a circle. I know, dah.
Thank you so much! You made me remember why I love Trig! I haven't felt that kind of excitement in ages!
I feel so stupid. I couldn't understand where you were getting the number for r. I'm so used to seeing r as the radius that it took my brain 30 mins to realize it didn't make since...because I forgot that diameter = 2 x radius. Younger me would be ashamed. ToT
Scott, quick question, is the semi-latus rectum of an orbit the altitude of a spacecraft when the vertical velocity equals the lateral velocity?
Also, can you go over bi-elliptic transfer orbits.
Also, is the eccentricity of an orbit the apogee altitude divided by the semi-major axis, and then have 1 subtracted from it?
I chose the wrong major in college, I should have went into physics rather than business. After one 13 minute video, I now understand orbital mechanics better than I have ever understood macroeconomics!
The number in question is at 4:42, at 300 km above the Earth's surface with the distance from earth's surface to it's center being 6,371 km should mean that the body in orbit is at 6671 km from the earth's center. Where did that extra 7 km come from?
Thank you, Scott! I am math graduate student but I was too lazy to dive deep into orbital mechanics. Can you tell me where to see the derivation of this v^2 formula from the gravity law?
Another small error: 8:53 must be "a becomes your geostationary radius", not "velocity".
for circular orbits
F=G*m*M/r²
ma=G*m*M/r²
a=G*M/r²
V²/r=G*M/r² (radial acceleration is V²/r)
V²=G*M/r
and then adapted to account for eccentricity to
V²=G*M*(2/r-1/((r1+r2)/2)
the derivation for that is here, derived using conservation of energy (en.wikipedia.org/wiki/Vis-viva_equation)
I think it would be helpful to explain the form of the equation relating altitude to velocity in an elliptical orbit as simply the conservation of total mechanical energy. As the satellite orbits, energy flows back and forth between kinetic (which goes as v^2) and potential (which goes as -GM/r) with a constant sum assuming no drag or perturbations.
202penguin As my understanding of the video has it this equation treats the body that the projectile is orbiting around as a point mass. That means that in a game such as kerbal space program R should indeed be your altitude plus half of kerbins diameter.
Nick Dunn I bought a fridge magnet in the KSC gift shop that originally said
What part of
GxmxM/R = mxVesc^2
Don't you understand? It's only rocket science!
A bunch of us, including some actual NASA rocket scientists, stood looking at this thing trying to figure it out. I realized it was probably designed by some English major who didn't know that you don't write 'x' for multiplication in algebra, and that you can cancel 'm' from both sides. So I corrected it to read
GM/R = Vesc^2/2
The left side gives the negative of the specific gravitational potential energy and the right side gives the specific potential energy (in joules/kg). When they're equal, the sum of the potential and kinetic energy is zero and the object has exactly enough velocity to escape.
Isnt the right hand side the specific kinetic energy?
TVTacon You are indeed right! My bad. What I should have said: the left side, GM/R, is -1 times the specific potential energy, energy per unit mass, due to the planet's gravity (potential energy is either 0 or negative, so the -1 makes it positive). The right side, V^2/2, is the specific *kinetic* energy. When V is escape velocity, they will be equal.
ApolloWasReal
Actually, I am a bit confused, I know you can easily find the orbital speed equation for a circular orbit with centripetal force, (mv^2)/r = GMm/r^2, but when you do it using convservation of mechanical energy you get 1/2 * m * v^2 = GMm/r, which gives you v^2 = 2GM/r, which is not just GM/r as it should be. Am I going crazy or something?
N.b. you can just say gravitational potential or g instead of specific gravitational potential energy, just abit easier to type haha.
Is it me or the ellipse at the start looks like a grumpy man ? Thank you for the physics lesson, I am a fresh subscriber and I really enjoy all your entertaining and instructing videos :)
Oh wow, more math videos please, this was great!
Please do more of these Scott Manley!
I thunk I was Smart...Then I watched this..:).. (very nice, keep em coming)
I don't understand any of this, but SCIENCE!
I was waiting for Brady from Numberphile to chime in.
Math, gah. It buuuuuuuurns.
I wish I wasn't so bad at it, since it's so useful like this.
Practice
I kept hearing "in the next video" so i went to look for it and didn't find it. I was very upset. Then I found out this video was uploaded 4 hours ago. Scott puts out a video more often than I change underwear.
You said geostationary orbit is ~42,000m up... I think you meant km!
Great video though, love leaning this stuff, hope you make more like this! I've always enjoyed using first principles to understand things, so the usual way many tutorials say you should do interplanetary transfers is to look up the angles in some calculator / reference or something, which annoys me... I want to understand WHY these angles are needed and HOW they were worked out!
Thank you for showing me this vid! I was able to launch my first geostationary satellite today. Much science.
This is great! I love it!
But I have a problem here:
Given a speed V at an altitude R orbiting a body of mass M, how can I calculate the semi major axis, periapse, and apoapse?
I found a way to find the semi major axis:
V^2 = GM(2/R-1/A) (as scott shows us)
V^2/GM = 2/R-1/A
V^2/GM-2/R=-1/A
-1/(V^2/GM-2/R)=A
I hope this is right, please correct me if it isn't
But then how do I calculate the pe and ap?
Scott Manley For the velocity at 5:00, I got 7729 m/s rather than your 7724 m/s. I'm guessing this is because we used different numbers for the radius of the Earth to convert from distance from surface to distance from center of gravity, but I would like to know what number you used. Was it Google's 6371 km, or Wikipedia's 6378.1 km? Or something else? I wasn't able to find the Earth's equatorial sea level radius anywhere...
He made a small math mistake, is that what could have caused this difference?
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