Physic Labs
Step 1 of 4: Central force → zero torque
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Intuition

Like a figure skater pulling her arms in to spin faster: with no external twisting force, the product 'distance × spin speed' stays fixed — closer to the center means faster rotation, farther means slower.

τ⃗=r⃗×F⃗grav=0 ⇒ L⃗=m r⃗×v⃗=const\vec{\tau} = \vec{r} \times \vec{F}_{grav} = 0 \ \Rightarrow \ \vec{L} = m\,\vec{r} \times \vec{v} = \text{const}
Analysis

Gravity always lies along the radius vector joining the planet to the Sun, so the cross product r⃗×F⃗\vec{r} \times \vec{F} vanishes for parallel vectors. Hence dL⃗dt=τ⃗=0\frac{d\vec{L}}{dt} = \vec{\tau} = 0 and L⃗\vec{L} is conserved.