Teams merge for dark-energy mission

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...

The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process called fusion. The principal source of energy in the sun is a net fusion reaction in which four hydrogen nuclei fuse and ultimately produce one helium nucleus and two positrons.
A helium nucleus has a mass that is 0.7% less than that of four hydrogen nuclei; this lost mass is converted into energy during the fusion. This reaction produces about...

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Considering a system that consists of n tiny particles, the angular momentum of any tiny particle may change, but the system's total angular momentum would remain constant. The principle of conservation of angular momentum only considers the net external torque acting on the system. While there are internal forces exerted by different particles within the system that also produce internal...

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...

The driving force for the motion of any vehicle is friction, but in the case of rocket propulsion in space, the friction force is not present. The motion of a rocket changes its velocity (and hence its momentum) by ejecting burned fuel gases, thus causing it to accelerate in the direction opposite to the velocity of the ejected fuel. In this situation, the mass and velocity of the rocket constantly change along with the total mass of ejected gases. Due to conservation of momentum, the rocket's...