When we think of how fast we're going (or the rate at which we're traveling) in a car, we usually express it in "miles per hour". This rate (miles/hr) is really reflecting the average distance that we've gone in the time it takes to travel that distance. For example, a car that travels 60 miles in 1 hour is traveling at a rate of 60 miles/hr. Alternately, a car that has a speed of 60 miles/hr will have traveled 60 miles in 1 hour. At this rate, in 2 hours it will have traveled a distance of 120 miles.
some basic information, like how fast an object is going (its speed
and how long it took to get to where it is now ( time),
it is possible to determine the distance that object has traveled.
This concept can be expressed as an equation that has the following form:
where D is the distance, R is the rate or speed, and T
is the elapsed time.
This basic idea can be applied to many situations. In the following exercises, you will calculate the distance to the moon ( TASK A), and the speed or rate of the Galileo Spacecraft on its way to Jupiter (TASK B ).
For the calculations we will perform in this lesson, we will be using the metric system. That is, we'll express distance in terms of kilometers and not miles .
Some useful relationships:
The Apollo 11 spacecraft was launched from Cape Kennedy at 13:31:01 GMT on July 16, 1969. After 2 hr and 33 min in Earth orbit, the S-IVB rocket engine was reignited for acceleration of the spacecraft to the velocity required to escape Earth's gravity. Although at times the spacecraft reached speeds near 40,000 km/hr, the average speed was about 5500 km/hr .
Lunar-orbit insertion began at 75:50 (75 hours and 50 minutes) ground elapsed time (GET). The spacecraft was placed in an elliptical orbit (61 by 169 nautical miles), inclined 1.25 degrees to the lunar equatorial plane. At 80:12 GET, the service module propulsion system was reignited, and the orbit was made nearly circular (66 by 54 nautical miles) above the surface of the Moon. Each orbit took two hours.
The lunar module (LM), with Astronauts Armstrong and Aldrin aboard, was undocked from the command-service module (CSM) at 100:14 GET, following a thorough check of all the LM systems. At 101:36 GET, the LM descent engine was fired for approximately 29 seconds, and the descent to the lunar surface began. At 102:33 GET, the LM descent engine was started for the last time and burned until touchdown on the lunar surface. Eagle landed on the Moon 102 hr, 45 min and 40 sec after launch.
ACTIVITIES: Using the above information and our D = R x T equation, can you calculated the distance to the moon?
If you would like to learn more about the Apollo 11 mission to the moon, try Apollo Facts .
Path of Spacecraft
If you'd like to learn more about navigating Galileo to Jupiter, check out:
|Distance from the Earth|
(millions of km)
(millions of km)
ACTIVITIES: Using the above table, which tracks the distance of the Galileo Spacecraft from the earth in January of last year, make two graphs:
Q: Looking at your first graph, is Galileo traveling away from or towards the Earth?
A: It is traveling towards the earth, since the Distance from the Earth is getting smaller as time progresses.
Q: What is the total distance Galileo has traveled in the month of January?
A: 36900000 km (or 36.9 million km's )
Q: What trends do you notice in looking at your graph of Date vs. the Distance Traveled?
A: The distance traveled is not constant, indicating that the spacecraft is speeding up.
Q: Calculate the Rate for Positions 3 and 5 in the above table.
A: 12 km/sec and 14.2 km/sec
HINT: Since rate is distance per time , divide the Distance traveled by the Elapsed Time . Remember to convert hours to seconds , and that the values in the table are millions of km's.
Sample Calculation, Position 2 :
How was the rate for Position 2 in the table calculated? Since distance divided by time is rate, we use the Distance Traveled and divide by Elapsed Time :
Rate = (11500000 km) / [(288 hours) x (60 min/hr) x (60sec/min)] = 11.1 km/sec
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Galileo Solid State Imaging Team Leader: Dr. Michael J. S. Belton
The SSI Education and Public Outreach webpages were originally created and managed by Matthew Fishburn and Elizabeth Alvarez with significant assistance from Kelly Bender, Ross Beyer, Detrick Branston, Stephanie Lyons, Eileen Ryan, and Nalin Samarasinha.
Last updated: September 17, 1999, by Matthew Fishburn
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