1. Spinning the solar nebula

Remember that the formula for angular momentum (L) is L = mvr, where m is the mass of the material, v is the orbital speed, and r is the distance from the center of the orbit. In the early history of the solar nebula, the nebula was large and spinning slowly. As the nebula collapsed, its rotation speed increased due to the conservation of angular momentum.

(a) Imagine some material orbiting the Sun today with an oribital radius of rnow. In other words, it is orbiting at a distance of rnow from the Sun. It will have an orbital speed of vnow. If that material originally had an orbit with a radius that was 1000 times larger than its orbital radius today, use the conservation of angular momentum to find the ratio vnow/voriginal. Show your work.

(b) In the solar system today, material that is 40 AU from the Sun has an orbital speed around 5 km/s. Use your answer to part (a) to find the orbital speed of this material when it was 40,000 AU from the Sun, before it fell inward with the collapse of the nebula.