Uploaded May 2026 | Updated September 2026, 3 weeks ago
In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m a, and his law on universal gravitation. While observing the Danish astronomer Tycho Brahe's astronomical observations, Kepler observed recurring patterns in the data, which he formulated as three laws:
1. A planet revolves around the sun in an elliptical orbit with the sun at one focus.
2. The line joining the sun to a planet sweeps out equal areas in equal times.
3. The square of the period of revolution of a planet is proportional to the cube of the length of the major axis of its orbit.
Isaac Newton later realized that Kepler's laws are merely the biproduct of his 2nd law of motion and his law on universal gravitation. I use Newton’s laws to derive Kepler's laws, while making extensive use of vector functions, calculus, and the polar equation of an ellipse.
Later in the video, I calculate the distance a satellite needs to be from the equator of the Earth to have a geosynchronous orbit, in which the orbit of the satellite around the Earth is in sync with Earth's rotation. This type of orbit is sometimes referred to as the Arthur C. Clarke orbit, named after the famous author of 2001: A Space Odyssey, who popularized the orbit in a fictional novel in 1945. I also go over some very interesting connections surrounding Arthur C. Clarke, so buckle up!
#math #vectors #calculus #astronomy #keplerslaws
Timestamps:
- Intro – 0:00
- Calculus book reference – 1:08
- Calculus Book Chapter – 1:25
- Topics to cover – 2:53
- Kepler’s Laws of Planetary Motion – 3:51
- Proof of Kepler's First Law: Planet revolves around the Sun in an ellipse – 6:46
- Applied Project: Kepler's Laws – 1:15:15
- Problem 1: Prove Kepler's Second Law – 1:17:26
- Problem 2: Prove Kepler's Third Law – 1:20:11
- Problem 3: Length of Earth's Orbit – 1:21:44
- Problem 4: Geosynchronous Satellite – 1:22:29
- Solutions to the Applied Project
- Solution to Problem 1: Prove Kepler's Second Law – 1:23:49
- Solution to Problem 2: Prove Kepler's Third Law – 1:52:58
- Solution to Problem 3: Length of Earth's Orbit – 2:16:28
- Solution to Problem 4: Geosynchronous Satellite – 2:27:05
- More info on Arthur C. Clarke – 2:46:05
- Outro – 3:00:00
Notes and playlists:
- Summary: inleo.io/threads/view/mes/re-leothreads-ypaeypzp
- PDF Notes: https://1drv.ms/b/c/88862ef47bcaf6cd/IQBB-MLn7NaERZF19kENFFUjAbBh7ZR_Qg_wQcBx0VB_Cb8
- Hive Notes: peakd.com/hive-128780/@mes/c3b94a80
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0FSh63mgXOKLQ41H4dkzbaY
- Vector Functions playlist: youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
------------------------------------------------------
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In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m a, and his law on universal gravitation. While observing the Danish astronomer Tycho Brahe's astronomical observations, Kepler observed recurring patterns in the data, which he formulated as three laws:
1. A planet revolves around the sun in an elliptical orbit with the sun at one focus.
2. The line joining the sun to a planet sweeps out equal areas in equal times.
3. The square of the period of revolution of a planet is proportional to the cube of the length of the major axis of its orbit.
Isaac Newton later realized that Kepler's laws are merely the biproduct of his 2nd law of motion and his law on universal gravitation. I use Newton’s laws to derive Kepler's laws, while making extensive use of vector functions, calculus, and the polar equation of an ellipse.
Later in the video, I calculate the distance a satellite needs to be from the equator of the Earth to have a geosynchronous orbit, in which the orbit of the satellite around the Earth is in sync with Earth's rotation. This type of orbit is sometimes referred to as the Arthur C. Clarke orbit, named after the famous author of 2001: A Space Odyssey, who popularized the orbit in a fictional novel in 1945. I also go over some very interesting connections surrounding Arthur C. Clarke, so buckle up!
#math #vectors #calculus #astronomy #keplerslaws
Timestamps:
- Intro – 0:00
- Calculus book reference – 1:08
- Calculus Book Chapter – 1:25
- Topics to cover – 2:53
- Kepler’s Laws of Planetary Motion – 3:51
- Proof of Kepler's First Law: Planet revolves around the Sun in an ellipse – 6:46
- Applied Project: Kepler's Laws – 1:15:15
- Problem 1: Prove Kepler's Second Law – 1:17:26
- Problem 2: Prove Kepler's Third Law – 1:20:11
- Problem 3: Length of Earth's Orbit – 1:21:44
- Problem 4: Geosynchronous Satellite – 1:22:29
- Solutions to the Applied Project
- Solution to Problem 1: Prove Kepler's Second Law – 1:23:49
- Solution to Problem 2: Prove Kepler's Third Law – 1:52:58
- Solution to Problem 3: Length of Earth's Orbit – 2:16:28
- Solution to Problem 4: Geosynchronous Satellite – 2:27:05
- More info on Arthur C. Clarke – 2:46:05
- Outro – 3:00:00
Notes and playlists:
- Summary: inleo.io/threads/view/mes/re-leothreads-ypaeypzp
- PDF Notes: https://1drv.ms/b/c/88862ef47bcaf6cd/IQBB-MLn7NaERZF19kENFFUjAbBh7ZR_Qg_wQcBx0VB_Cb8
- Hive Notes: peakd.com/hive-128780/@mes/c3b94a80
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0FSh63mgXOKLQ41H4dkzbaY
- Vector Functions playlist: youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .
------------------------------------------------------
Become a MES Super Fan! youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
