Angular momentum is conserved. If we know the distance and velocity of planets i

Question

Angular momentum is conserved. If we know the distance and velocity of planets in orbit, we can discover the angular momentum of the planet. This is easier to do when the planet is at its perihelion (nearest point to the Sun) or aphelion (farthest point from the Sun). For example, look at this sample planetary data:^Hermitian Matrix What is the angular momentum of each planet? For Earth: v = speed of Earth at perihelion = v_circled plus r = distance of Earth at perihelion = r_circled plus m = mass of Earth = M_circled plus (in kg) v vector = (+v y) m/s r vector = (+r x)m For Jupiter: v = speed of Jupiter at perihelion = v r = distance of Jupiter at perihelion = r m = mass of Jupiter = M (in kg) v vector = (+v y) m/s r vector = (+r x)m

Explanation / Answer

The angular momentum L of an object of mass m moving in elliptical orbit is given by

L = m*v1*r1 = m*v2*r2

for jupiter L = 1.8983 x 10^27 * 13720* 740679835 = 1.9290 x 10^40 kg-m2/s

for earth L = 5.9726 x 10^24 * 30300 * 147098291 = 2.66 x 10^37 kg-m2/s

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