You will be able to
- Explain how Kepler's three laws and Newton's laws together describe satellite orbits
- Calculate orbital speed changes using delta-V and predict how a burn reshapes an orbit
- Identify the six orbital elements and what each one specifies about an orbit
- Relate orbital inclination to launch site latitude and launch azimuth
- Compare Hohmann, geosynchronous, Molniya, and sun-synchronous orbits by their purpose and tradeoffs
Good to know first
- Basic understanding of force, mass, and motion
- Familiarity with latitude, longitude, and the equator
- Comfort reading simple algebraic formulas
Syllabus
10 lessons
- 1
Early astronomy: from geocentric to heliocentric views Free
This lesson shows how people's picture of the universe changed from Earth at the center (geocentric theory) to the Sun at the center (heliocentric theory). It also introduces orbital mechanics, the study of how objects move around other objects, which is used today to plan spaceflight.
3 exercises3 questions - 2
Kepler's Three Laws of Planetary Motion Beyond Pass
Kepler's three laws describe how planets and satellites move: they follow ellipses with the central body at one focus, they sweep equal areas in equal times (so they speed up near the body and slow down far away), and the square of the period grows with the cube of the mean distance. The lesson shows how each law applies to Earth satellites.
2 formulas3 exercises3 questions - 3
Newton's laws and universal gravitation Beyond Pass
This lesson shows how Newton's law of universal gravitation and his three laws of motion explain why a satellite stays in orbit and how a rocket gets off the ground. Kepler described how orbits look; Newton explains why they happen and gives the equations used to calculate them.
- 4
Orbits as continuous falling, and escape velocity Beyond Pass
A satellite is a projectile that keeps falling around the Earth without ever landing. Firing faster changes the path, and at escape velocity (about 7 miles per second at the surface) the projectile can leave Earth's gravity for good.
3 exercises3 questions - 5
The six orbital elements and the coordinate system Beyond Pass
This lesson shows how six numbers, the orbital elements, fully describe a satellite's orbit: its size, shape, orientation and the satellite's position along it. It also explains the geocentric equatorial coordinate system those numbers are measured in.
2 formulas2 exercises4 questions - 6
Ground tracks and orbital precession Beyond Pass
A ground track is the path a satellite's position traces on the rotating Earth's surface, and it shifts westward on each orbit. Two causes drive the shift: Earth's rotation beneath the orbit, and precession of the orbital plane caused by Earth's equatorial bulge.
2 exercises4 questions - 7
Launch site latitude, inclination, and Earth's rotation Beyond Pass
You will learn why the latitude of a launch site sets the smallest orbital inclination you can reach directly, and how launch direction (azimuth) changes that inclination. You will also see why launching from near the equator gives a rocket a free eastward speed boost from Earth's spin.
3 exercises4 questions - 8
Launch windows and multi-stage launch vehicles Beyond Pass
A launch window is the short time interval when a rocket can lift off so that the spacecraft reaches its planned orbit and meets all mission conditions. Multi-stage launch vehicles burn in stages, dropping spent parts to shed weight, as the Space Shuttle does with its boosters and external tank.
4 exercises4 questions - 9
Delta-V: changing an orbit with a burn Beyond Pass
Delta-V is the change in a spacecraft's velocity produced by an engine burn, and it sets how much fuel the burn costs. A forward (prograde) burn raises the orbit and a backward (retrograde) burn lowers it, and any burn point is revisited on every later pass.
3 exercises3 questions - 10
Hohmann transfers and orbital plane changes Beyond Pass
This lesson shows how two burns can move a spacecraft between two circular orbits in the same plane using the fuel-efficient Hohmann transfer, and how thrust out of the orbital plane changes inclination. It also explains why plane changes are so expensive in fuel.
3 exercises4 questions
Free preview · Lesson 1 in full
Early astronomy: from geocentric to heliocentric views
This lesson shows how people's picture of the universe changed from Earth at the center (geocentric theory) to the Sun at the center (heliocentric theory). It also introduces orbital mechanics, the study of how objects move around other objects, which is used today to plan spaceflight.
Draw and write next to the video.
The idea
For thousands of years, people watched the stars and planets move across the sky and tried to explain why. The ancients believed the Earth was flat. Around 350 BC, Aristotle argued from evidence that the Earth is round. Around 150 AD, Ptolemy presented the geocentric theory: the Earth is stationary at the center of the universe, and the Sun, Moon, stars and planets all revolve around it in complicated orbits.
The geocentric model could describe the sky, but its paths were very complex. In the 1500s, Nicholas Copernicus of Poland presented the heliocentric theory. In this view the Sun sits at the center, and the Earth revolves around the Sun while it also rotates on its own axis. This simpler picture changed how astronomers thought about the motion of planets.
The study of how planets and other bodies move under gravity grew from this work into a field called orbital mechanics. Today orbital mechanics is the science behind spaceflight: engineers use it to put satellites into orbit around the Earth and to send spacecraft beyond our solar system.
A simple way to remember the two views: in the geocentric picture, everything circles the Earth; in the heliocentric picture, the planets circle the Sun, and the Earth is one of those planets. The same star patterns you see at night fit both models, but the explanation of their movement is very different.
Key points
- Aristotle showed, around 350 BC, that the Earth is round, not flat. 0:48
- Geocentric theory (Ptolemy, about 150 AD): the Earth is stationary at the center and everything else revolves around it. 0:56
- Heliocentric theory (Copernicus, 1500s): the Sun is at the center and the Earth revolves around it while rotating on its axis. 1:12
- The Earth is a planet moving around the Sun in the heliocentric view, and the Sun is the center of the system. 1:24
- Orbital mechanics grew out of this study of planetary motion and is now applied to spaceflight and satellites. 1:32
Words to know
- Geocentric
- Earth-centered. The Earth sits still in the middle and everything else circles it.
- Heliocentric
- Sun-centered. The Sun is in the middle and the Earth and other planets circle it.
- Orbit
- The path one object takes around another, such as the Earth around the Sun.
- Orbital mechanics
- The study of how objects move around other objects under gravity. It is used to plan spaceflight.
- Rotate
- To spin around your own axis. The Earth rotates while it also revolves around the Sun.
Watch out
- Mixing up the two names: geocentric = Earth in the center, heliocentric = Sun in the center.
- Mixing up 'revolve' and 'rotate'. In the heliocentric view the Earth revolves around the Sun and also rotates on its own axis.
- Subtracting BC and AD dates as if they were on the same side. 350 BC and 150 AD are on opposite sides of year 1, so you add them.
Practice
In your own words, explain the difference between the geocentric and heliocentric theories. Then say what orbital mechanics is used for today.
Hint
Ask yourself: what is in the center in each theory, and what moves around it?
Solution
- Geocentric: Earth is at the center and the Sun, Moon, stars and planets revolve around it.
- Heliocentric: the Sun is at the center and the Earth (and other planets) revolve around it.
- Orbital mechanics grew out of the study of planetary motion. It studies how objects move around other objects under gravity, and it is used to plan spaceflight.
Model answer: In the geocentric theory, the Earth is the fixed center and everything else circles it. In the heliocentric theory, the Sun is the center and the Earth is one of the planets moving around it. Orbital mechanics grew out of this study of motion. Today it is used to put satellites into orbit and to send spacecraft through space.
Draw two simple diagrams on your scratchpad: one showing the Earth at the center with the Sun and planets circling it, and one showing the Sun at the center with the Earth and planets circling it. Label each with its theory name.
Hint
Start with the object in the middle, then draw the others as small circles around it, with arrows.
Solution
- Draw a circle in the middle and label it Earth. Draw the Sun and planets as small circles around it with arrows showing they circle the Earth. Label it geocentric.
- Draw a circle in the middle and label it Sun. Draw the Earth and planets as small circles around it with arrows. Label it heliocentric.
Two labelled diagrams: Earth at the center for geocentric, Sun at the center for heliocentric.
Aristotle argued that the Earth is round around 350 BC, and Ptolemy presented the geocentric theory around 150 AD. About how many years apart were these two events?
Hint
350 BC is before year 1 and 150 AD is after it. The dates are on opposite sides, so add them.
Solution
- 350 BC is 350 years before year 1.
- 150 AD is 150 years after year 1.
- Total gap: 350 + 150 = 500 years (about).
500 years
On your scratchpad
Draw two small diagrams side by side: on the left, the Earth in the middle with the Sun and planets circling it; on the right, the Sun in the middle with the Earth and planets circling it. Label them geocentric and heliocentric.
Quiz
According to the geocentric theory presented by Ptolemy, what is at the center of the universe?
- The Sun
- The Earth
- Jupiter
- The Moon
Show the answer
B. The Earth · Geocentric means Earth-centered. The Earth is stationary at the center, with the Sun, Moon, stars and planets revolving around it.
0:56 watch the momentWho presented the heliocentric theory in the 1500s?
- Aristotle
- Ptolemy
- Nicholas Copernicus
- Isaac Newton
Show the answer
C. Nicholas Copernicus · Nicholas Copernicus of Poland presented the heliocentric theory, in which the Earth revolves around the Sun.
1:12 watch the momentWhat is the heliocentric theory?
- The Sun revolves around the Earth
- The Earth is flat and stationary
- The Earth revolves around the Sun while rotating on its axis
- The stars are fixed to a sphere around the Earth
Show the answer
C. The Earth revolves around the Sun while rotating on its axis · In the heliocentric theory the Sun is the center, and the Earth revolves around it as it rotates on its axis.
1:18 watch the moment
Lessons 2–10
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Made by Beyond from the video “Space Flight: The Application of Orbital Mechanics” by NASA STI Program. The video plays in YouTube's own player. Watch it on YouTube · All lessons