Math in the NewsIssue 76

Back to the Moon!In this issue we analyze NASA’s recently launched LADEE Mission.

The LADEE (Lunar Atmosphere and Dust Environment Explorer) is NASA’s latest rocket to the Moon. This lunar probe will analyze the Moon’s atmosphere. See a brief animation here.http://www.youtube.com/watch?v=mEutj2kDylE

The challenge with all space travel is getting a massive rocket into space.

This involves accelerating, or changing the speed of the rocket. This is shown in the speed-vs-time data for the LADEE Mission.

There are two ways a rocket accelerates into space. One is obvious, the other one more subtle.

The first way a rocket accelerates is through the thrust from the rocket propulsion.

There is a downward force from the burning fuel ejecting from the bottom of the rocket. But how does this help to lift the rocket?

According to Newton’s Third Law of Motion, an equal and opposite force pushes the rocket upward.

Momentum is defined as the mass of an object times its velocity. In the rocket liftoff situation momentum is conserved.

We can use the momentum equation to solve for the speed of the rocket.But notice that because the rocket is so much more massive, the change in the rocket’s speed is miniscule. As a result, the rocket needs A LOT of fuel to accelerate it.

As a rocket burns through its fuel, it loses mass. This decrease in mass has a beneficial effect. It, too, helps accelerate the rocket. This is the second way a rocket accelerates into space. This also changes the momentum equation.

The change in speed for a rocket when launched from the Earth is found using this equation. Using this equation allows scientists to calibrate the amount of fuel needed for a trip.

Conclusions

• A rocket’s acceleration is based on the thrust from its rocket fuel.

• The loss of mass from burnt rocket fuel helps the rocket gain more speed.