Length of Earth's Orbit around the Sun is 299 million km wide

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In this video, I use Kepler's third law to calculate the length of Earth's elliptical orbit to be around 299,000,000 km wide and takes about 365.25 days to complete 1 full revolution. The equation for Kepler's 3rd law shows that the square of the period of revolution is proportional to the cube of the length of the semi-major axis (half the major axis) of the ellipse. The proportionality constant only depends on the mass of the Sun and the gravitational constant. Thus, we can calculate the major axis of any planet just by knowing how long it takes to revolve around the Sun!

#math #vectors #calculus #ellipse #keplerslaws

Timestamps

• Applied Project Problem 3: Length of Earth's Orbit – 0:00
• Solution: First, convert Earth's period of 365.25 days to seconds – 0:41
• Plug in the period into Kepler's 3rd law to obtain the cube of the semi-major axis – 3:59
• The length of the major axis is twice the semi-major axis – 7:18
• Calculation check with OneNote’s built-in calculator – 8:19

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