Hey, guys. So remember when we were talking about satellite motion, we said that there was a specific velocity a satellite needed in order to go in a perfectly circular orbit. Well, you're going to need to know how to use that formula and calculate that velocity. So let's go ahead and cover that in this video. We have a satellite that's out at some distance away from the Earth. That center of mass distance is little r. At that distance, there is a gravitational force that constantly tries to pull it back towards the Earth. So the question is why does it just come crashing into the surface? Remember that the satellite is actually falling towards the Earth, but it has a tangential velocity that basically keeps it going in a circle. This thing is constantly falling around the Earth, and the Earth is trying to pull it backward, but that tangential velocity keeps it going, so the Earth is constantly curving beneath it. Okay. And so, for a satellite in circular orbit, that gravitational force is actually what's causing it to go in a circle. That gravitational force keeps the satellite going in uniform circular motion. And the relationship between that speed, which is the orbital speed, and the distance, which is that little r, is the vsat equation. That is the square root of capital G capital M over little r. I just want to remind you guys that that capital M is actually the mass of the big planet that it's going around, not the mass of the satellite. And that little r is not the radius, it's the orbital distance. It's that little r distance away. Sometimes you're going to need to know where that equation comes from, so I can actually go ahead and work it out for you really quickly. How do we get the velocity from uniform circular motion? Well, remember that if this is the force that's acting on it and it's going uniform circular motion, then it has a centripetal acceleration, so we can start from F = ma to get to this. We know that F = ma, but all these forces are centripetal. So the sum of all centripetal forces equals m ac. Now we know the only force that's acting on this is the force of gravity, and that is m. The ac comes v2 over r. So this is where this velocity actually comes from. Now we know what this force of gravity is. It's just G big M little m over r2, that's just Newton's Law of Gravity. And that's equal to mv2 over r. So to figure out what this v2 is, let's go ahead and simplify this equation. I've got little m that appears on both sides, so I can cancel that out, and I've got little r that also appears on both sides. And so what I'm left with is I'm left with capital G capital M over r equals v2. So, if I take the square roots, I'm just going to get to that Gm over r. I'm going to get to that vsat equation. So again, that is, the relationship between the orbital speed and the orbital distance vsat in order to keep this thing going in circular motion. So for instance, this satellite out here that's at some distance r has an exact v in order to keep it going in a perfect circle. Anything more or less than that, it's not going to be perfectly circular. And also if I wanted to change this orbit, if I wanted to go out farther or if I wanted to push this thing in closer, my vsat would have to change in order to keep this thing traveling in a perfect circle. So that's what that means. Alright, guys. Let's go ahead and work out an example for this with the International Space Station. So we're asked to find the height of the International Space Station, which travels around the Earth. And we're told that the orbital speed is 7,670 meters per second in a nearly circular orbit. So anytime you see this word nearly circular, you're just going to assume that they're talking about a circular orbit, so you can use all these equations to do that. Okay. So what are we told? We're actually trying to figure out what the height of this thing is. But remember that whenever we're trying to find little h or big R, we're always going to find little r first. And then we can relate it using the r equals big R plus h formula. So, first, we have to find little r. So how am I going to do that? Which equation am I going to use? I'm trying to find what little r is, and I'm only told what the velocity of the satellite is. So I can use the vsat equation to relate those two things because those are the only two variables that pop up in that equation. So let's start from the vsat equation. So I've got vsat equals square root of GM over r. So now, I want to actually get to what this r is, so then I can basically get to what h is. So I just have to, I'll go ahead and isolate that. I've got this r that's trapped in the denominator here, so I can lift the square roots by taking the square of both sides. So I've got vsat2 equals GM over r. And now if I want to get r by itself, I basically want this thing to come up, and I want the vsat to come down. So these things are just going to trade places. So I've got that r equals GM over vsat2. And now I just have to make sure I have all of those numbers. Right? I have G, I have M, and I have vsat2. And that capital M, because I'm going around the Earth, is just the mass of the Earth, which I have in this table right here. So, plugging all that stuff in, I get 6.67 times 10 to the minus 11. And I've got the mass of the Earth, 5.97 times 10 to the 24th. Oops. Times 10 to the 24th, and then divided by 7,670. Just make sure that you square that in the denominator. And you should get 6.77 times 10 to the 6th, and that's in meters. But just remember that we're not quite done yet because that was, we've only solved, oops. We've only solved for little r. Now we have to go and plug it back into this equation to solve for h, which is the height. So we have little r equals big R plus h. So, if we want to find h, we have to set, we have to isolate h. So h is equal to little r minus big R. So I've got 6.77 times 10 to the 6th minus, what's this what's this big R? Well, this big R, if we're talking about the Earth, is just the radius of the Earth. So we're going to have them subtract that, 6.37 times 10 to the 6th, and we should get 4 times 10 to the 5th, which is about 400 kilometers. You can actually go ahead and Google this. If you Google the height of the International Space Station orbit, you'll find that it is about 400 kilometers on average. It goes up and down a little bit, but that's pretty much what it is on average, which is pretty cool. So we can use some F = ma and some simple equations to figure out how high the International Space Station actually orbits around the Earth, which is pretty cool. Alright, guys. Let me know if you have any questions with this.
Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m
- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m
- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 54m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy32m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m
- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m
- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m
- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m
- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m
- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m
- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
8. Centripetal Forces & Gravitation
Satellite Motion: Speed & Period
Video duration:
6mPlay a video:
Related Videos
Related Practice
Satellite Motion: Speed & Period practice set
- Problem sets built by lead tutorsExpert video explanations