Associated Topics || Dr. Math Home || Search Dr. Math

### Relative Motion on Face of Earth

```Date: 05/06/2007 at 05:18:18
From: Kaitlyn
Subject: (no subject)

If I am traveling at the same rate of speed that the earth is moving
in the opposite direction then would it look like I was not moving
looking at the earth from space?

I am nine years old and in the third grade.  I have looked on the NASA
site and can't find it.  I have also tried to make a model but can't
get the two speeds to be the same.

```

```

Date: 05/07/2007 at 09:12:09
From: Doctor Rick
Subject: Re:

Hi, Kaitlyn.

The earth turns on its axis once a day; it turns toward the east
(counterclockwise if you look from above the north pole).  The idea,
then, is that you walk westward along your line of latitude (that
is, keeping your latitude--distance from the equator--constant).  You
walk at such a speed that you make it back home in one day.

Picture the same sort of thing on a merry-go-round or carousel.
(Don't really try it, it isn't safe!)  First imagine that the merry-
go-round is not moving, and you walk to the left along the edge so
that you take one minute to get back where you started.  Then imagine
that the merry-go-round starts moving to the right, and its speed is
such that it takes one minute to go around once.  You repeat your
walk; you get back to the horse where you started just as that horse
gets back around to where *it* started.

Now imagine your friend standing next to the merry-go-round, on the
ground.  At the beginning you are next to your friend; at the end of
one time around, you are next to your friend.  Where were you in
between those two times?  Think about it ... maybe a little model
will help.

By the way, though you don't need to know your speed in order to
answer the question, it *is* interesting to find out.  Suppose you're
on the equator.  How long is the equator (the circumference of the
earth)?  How long will the trip take?  Can you convert the speed to
miles per hour (or kilometers per hour)?  Is "walking" a good way to
describe it?

Also, there are some tricky little issues if you want a full answer
to your question about looking at the earth from space.  It has to do
with whether that observer is comparing your movement with the sun
or the stars, and it has to do with two different ways a "day" can
be defined.  Also, even if you're not moving with respect to the
earth, the earth itself is moving around the sun, so you'll move
once around the sun in a year.  You can't really be stationary in any
real sense as long as you're on the earth.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/

```

```

Date: 05/20/2007 at 03:31:30
From: Kaitlyn
Subject: Thank you ((no subject))

Thank you very, very much for helping me with this problem.  It has
been bugging me for about a year and no one I knew could help me.
```
Associated Topics:
Elementary Three-Dimensional Geometry
High School Higher-Dimensional Geometry
Middle School Higher-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search