the mathematics of space rendezvous l.
Skip this Video
Loading SlideShow in 5 Seconds..
The Mathematics of Space Rendezvous PowerPoint Presentation
Download Presentation
The Mathematics of Space Rendezvous

Loading in 2 Seconds...

play fullscreen
1 / 40

The Mathematics of Space Rendezvous - PowerPoint PPT Presentation

  • Uploaded on

The Mathematics of Space Rendezvous. NASA has a variety of classroom activities designed to accompany the video. Click here to explore. Overview. The NASA video illustrates the use of algebra and estimation in shuttle flight and rendezvous.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'The Mathematics of Space Rendezvous' - Ava

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
the mathematics of space rendezvous

The Mathematics of Space Rendezvous

NASA has a variety of classroom activities designed to accompany the video. Click here to explore.

  • The NASA video illustrates the use of algebra and estimation in shuttle flight and rendezvous.
  • The accompanying slides demonstrate the problems that the astronauts pose and provide extra support as the problems are worked.

NASA has developed a learning guide to accompany this video.


Have you ever missed an appointment?

  • How did it make you feel?
  • How did it make the other party feel?
  • What is a rendezvous?See the video for definitions.
  • How can you plan ahead to get there on time?
  • How do astronauts calculate where and when to meet in space?
math the language of the universe
Math… The Language of the Universe
  • Mathematics is an essential part of space travel.
  • Mathematics even helps us travel on earth.

It is more than numbers and symbols!

math the language of the universe6
Math… The Language of the Universe
  • What instruments did early space travelers use to calculate mathematical equations?
  • What instruments do space travelers use today to calculate mathematical equations?
math aboard the space shuttle
Math aboard the Space Shuttle
  • The Shuttle Design
  • The Launch
  • Navigation
  • The Landing
  • The Rendezvous



Can you think of examples of rendezvous?

  • Is like playing frisbee catch with a dog.
  • Is like a quarterback throwing a timing route pass to a wide receiver.

First: What question needs to be answered?

When will the target (the Mir) be at the rendezvous site (over Moscow)?

the target
The Target

Gather the known facts:

  • Altitude of 400 kilometers.
  • Orbit is at 92 minutes.
  • Incline of the orbit is 51.6’.
  • Earth revolves once every 24 hours.


Find out more about the Mir.

the target12
The Target

More facts:

  • Moscow is at 37’ E longitude.
  • Mir’s present longitude is at 105’ E.

Review the questions again:

  • When will the target be at the rendezvous site?
  • When will it pass overthe rendezvous site?

Check out where the space station is right now on this real time site.


What other information do we need to solve this problem?

Degrees the earth rotates in the time it takes Mir to make one orbit.

set up the equations
Set Up the Equations

Recall known and previous given facts:

  • 360° in a full circle or around the earth.
  • The earth rotates once in 24 hours.
  • Mir’s orbit takes 92 minutes.


set up the equations16
Set Up the Equations
  • The following ratio determines how far the Earth rotates with each orbit of the Mir360° = x

24 hours 92 min

  • We need these in common terms, let’s change the hours into minutes.

(24 hours is 1440 minutes)

  • Here is the problem again:360° = x

1440 min 92 min


What other information do we need to solve this problem?

  • How far it is between Moscow and where the space station is currently.
  • The angular distance between the Mir’s present locationand its rendezvous point is 105o – 37o or 68o.

What other information do we need to solve this problem?

  • How long it takes Mir to make one orbit.
  • We were given this information earlier.Mir’s orbit takes 92 minutes.
  • X = 92 min x 360o= 23o

1440 min

  • The Earth rotates 23o each time Mir circles it once.
  • To rendezvous at the designated location, the Earth must rotate 68o.
  • Mir must circle Earth.











  • If it takes 92 min per orbit, then

3 orbits x 92 min = 276 min = 4.6 hrs


orbital altitude
Orbital Altitude

How does orbital altitude affect an objects travel?

  • Speed
  • Orbit
  • Rendezvous
  • How fast is Mir traveling in its orbit?
  • How fast is the shuttle traveling?
  • How can be at the same place and match speed?


gather the facts
Gather the Facts
  • Mir’s altitude is 400 km and speed is 92 min/revolution.
  • The shuttle’s altitude is 298 km and speed is 89 min/revolution.
  • The Earth’s radius is 6,378 km.
known facts
Known Facts
  • Orbit is almost a circle
  • Circumference of a circle

C = 2r


known facts25
Known Facts

Equation for speed

Speed = Distance/Time

mir s orbit
Mir’s Orbit
  • First the formula:Speed = C (Mir’s orbit) / R (minutes)
  • Then the facts:Mir orbits at a distance of 6,378 + 400 km
  • Find Mir’s orbit:C (Mir’s orbit) = 6,778 km x 2(pi)

= 42,578 km per orbit.

mir s speed
Mir’s Speed
  • The formula again:Speed = C (Mir’s orbit) / R (minutes)
  • Put in Mir’s orbit:Speed = 42,587 km/92 min
  • Solve the equation:Speed of Mir = 463 km/min = 27,780 km/hr
speed of the shuttle
Speed of the Shuttle
  • First the formula:Speed = C (shuttle) / R (minutes)
  • Find the shuttle orbital radius:637 km x 298 km = 41,947 km
  • Put in the facts:Speed = 41,947 km / 89 min
  • Calculate: Speed of the Shuttle = 471 km/min = 28,260 km/hr
slow down to rendezvous
Slow Down to Rendezvous
  • The space shuttle must slow down to rendezvous with Mir.
  • To slow down, the shuttle will climb to Mir’s higher orbit.
gather the facts30
Gather the Facts
  • 0.4 meters per second increase in velocity equals 1 km increase in altitude.
  • Present altitude is 298 km.
  • Need to increase altitude to 305 km.

How many meters per second does the shuttle need to increase to rise 7 km?


set up the equations32
Set Up the Equations

An increase of 2.8 m/s will increase the orbit

of the shuttle 7 km and actually slow it down!

Desired – current = needed increase in altitude

305 km – 298 km = 7 km

Recall: 0.4 m/s increase in velocity = 1 km increase in altitude .

7 (km) / 1 (km) x .4 (m/s) = 2.8 m/s

shuttle instruments
Shuttle Instruments
  • Shuttle instruments can show this process graphically.
  • The astronauts can also see the Mir through the windows.


Virtual view of Mir through the shuttle window.

views from space
Views from Space

The video is showing videos that were taken by the astronauts. More videos and photos are available at NASA’s web site.


Click on this slide to see more photos.


it takes math to rendezvous in space
It takes Math to Rendezvous in Space

The astronauts use both:

  • Computer calculations
  • Math estimation skills

Try another math activity with airplanes.

math of the universe
Math of the Universe

Whether it is using scientific notation to measure the microscopic or astronomic, whether it is estimation or calculus, mathematics plays a big part in science.

Read more about experiments performed aboard the shuttle and space station.

math on earth
Math on Earth

The video is showing some examples of everyday activities that need math. Can you think of others?

Explore a web site with activities focusing on every day math.

math and rendezvous
Math and Rendezvous
  • The video and slides have illustrated a few problems that the space shuttle astronauts need to estimate while on a single space flight.
  • Space travel and travel on earth have similarities. Work with your class to create earth examples of rendezvous.
math and rendezvous39
Math and Rendezvous

Math is an important part of making meetings in space and on earth prompt and accurate.


The Technology Leadership Institute (TLI) is funded by the United States Department of Education's Preparing Tomorrow's Teachers to use Technology (PT3) Program (Catalyst grant - P342A990323).