National Aeronautics and Space Administration Logo
Follow this link to skip to the main content NASA Banner
Solar System Exploration
Return to Solar System Exploration
Facebook Twitter YouTube Facebook Twitter YouTube Flickr iTunes
Follow Us
Impact Velocity
Fun Facts  |  Model Kits  |  Color Page  |  Comet Quiz  |  Can You Answer This? 
Brain Twisters  |  Mission Challenge  |  Special Organizations  |  Name That Game 

Discovery Zone - Mission Challenge

See National Math Standards for this Challenge.

Q: How fast will the impactor spacecraft be moving when it hits Tempel 1?

In one way this is a bit of a trick question. Since both the comet and the impactor spacecraft will be moving in nearly the same orbit at the time of impact, what is important really is how fast the impactor spacecraft will be traveling relative to the comet. As an example of the importance of this difference, consider two cars involved in a rear-end collision. If both cars are moving at the time they collide, it isn't the velocity of the first car or the second car that would be used to calculate the energy of impact, it's the difference between them. So a car traveling at 60 mph striking a car traveling 55 mph transfers the same amount of energy at collision as a car traveling 5 mph striking a stationary car.

Another complication that has to be taken into account is the fact that the comet and impactor spacecraft will be moving through three-dimensional space, instead of the "one dimensional" space of the car example. Fortunately this can be fixed by thinking of the motion one piece at a time, using vectors.

3D Axes

If you assign the same x-y-z set of axes for both objects, their movement can be broken down into three components, an x-component, a y-component and a z-component. This gives you the velocity that the object is moving along that axis. The overall velocity of the object can be determined by simply adding up the vectors. Since the three vectors will be at right angles to each other (since they're along the three right-angle axes), we can just use the three dimensional form of the Pythagorean theorem:

Pythagorean Theorem (v squared equals x squared plus y squared plus z squared)

Vectors representing the velocity of two cars

Looking back at the car example, let's say that the cars were moving along the x-axis. This means that their velocities (in mph) along the three axes would be:
     Car 1: (60, 0, 0)
     Car 2: (55, 0, 0)

This means that the overall velocities of the cars would be:

Car 1: Equation for velocity of Car 1 = 60 mph

Car 2: Equation for velocity of Car 2 = 55 mph

Okay, enough hints. The last piece of information you need is the x, y, and z velocities (in kilometers per second) for the comet (27.09, -11.40, -5.46) and the impactor spacecraft (18.41, -12.67, -0.16). From these, can you determine the velocity of the impactor spacecraft relative to the comet at the time of impact?

Click here for the answer...

Awards and Recognition   Solar System Exploration Roadmap   Contact Us   Site Map   Print This Page
NASA Official: Kristen Erickson
Advisory: Dr. James Green, Director of Planetary Science
Outreach Manager: Alice Wessen
Curator/Editor: Phil Davis
Science Writers: Courtney O'Connor and Bill Dunford
Producer: Greg Baerg
Webmaster: David Martin
> NASA Science Mission Directorate
> Budgets, Strategic Plans and Accountability Reports
> Equal Employment Opportunity Data
   Posted Pursuant to the No Fear Act
> Information-Dissemination Policies and Inventories
> Freedom of Information Act
> Privacy Policy & Important Notices
> Inspector General Hotline
> Office of the Inspector General
> NASA Communications Policy
> NASA Advisory Council
> Open Government at NASA
Last Updated: 28 Jun 2010