Sometimes we see things differently, depending on where we're located. For example, suppose someone passes by in a car and drops a ball out the window of the car. Can you describe the path of the ball?

If you are a pedestrian standing on the sidewalk, the ball will follow a parabolic path to the ground. From the frame of reference of the person standing on the sidewalk, the ball is seen to move in a path whose shape is a parabola.


Here's the path of the ball all by itself, as seen by the person on the sidewalk. It is clearly moving in a parabolic path.

This is because it is not only accelerating downwards, but is also moving to the left with the speed of the car, a speed it had when it was dropped. It has a constant leftward velocity, and an accelerating downward velocity.



So far, so good. But is there any other way to describe the ball's path?
Imagine what the person inside the vehicle will see, as he looks at the ball he has dropped. He is moving forwards with the ball.

From the frame of reference of the person in the car, the ball is seen to accelerate straight downwards.

Which answer is correct?

Here's what most people will say. "The person who is in the car and moving forwards with the ball seems to see it fall straight down, but if you watch the ball's path from a stationary location, it can be seen to move in a parabolic path. Since that observer is standing still, the parabolic path is the true path of the ball".

Logical? It might seem so, but actually the conclusion just above is completely wrong.


There is no 'true' path of the ball. How it seems to move depends entirely upon where you are.

In other words, how you describe the path of the ball depends on your frame of reference. If you are in the car, you will see the ball fall straight down. If you are at the side of the road, you will see the ball follow a parabolic path. Both descriptions are equally true.

About now you've probably decided that we're just playing with words. The ball might seem like it's falling straight down when you look out the window of the car, but really it follows a parabola, because the person standing still saw it that way.

Guess what!? The person isn't standing still!


In the frame of reference of the surface of the earth, the person is standing still. But there are other frames of reference where that person is moving, and so is the ball.

For example, the earth is rotating. To a person sitting 'stationary' in space above the North Pole, who can see the ball through a telescope, the ball is seen to move in a circle, in addition to its falling motion. This is also a true motion of the ball.

From this person's frame of reference, the ball follows a huge circular path as the earth turns, as well as a tiny parabolic path when the person drops it from the car.

But that observer, while stationary with respect to the earth, isn't really stationary either! Imagine you're an observer sitting above the plane of the solar system, watching the earth move around the sun. You're stationary with respect to the solar system, and will be able to watch the earth, and the ball with it, move around the sun.



Now how would you describe the motion of the ball? (You can see it through a powerful telescope).

Clearly it's moving in a complicated path, mostly in a very large circle around the sun, once every 365 days.

It actually follows little 'loops' as the earth rotates at the same time. The path of the ball on the surface of the earth, as the earth rotates and moves around the sun, is shown in more detail in the diagram at the right, for several days of the year. .The tiny parabola as the ball is dropped from the car can't be seen on this scale.
This is a true motion of the ball, as described by someone in space at rest above the solar system. From their frame of reference, the ball is following this complicated path.



Wait, there's more!

The sun is also moving, with other nearby stars, within a huge cluster of stars on our local arm of the Milky Way galaxy. An observer located well outside our solar system (and not moving relative to us) would see our sun, and the earth orbiting around it, moving past in a path similar to what you see on the left. On this scale, the rotation of the earth and the falling ball are too small to be noticeable.
And that cluster of stars itself is moving around our galaxy as it rotates. And our whole galaxy is moving within our local cluster of galaxies ... and that cluster of galaxies is moving outward as the universe expands ...



The sun moving within our galaxy. Once around takes 200 million years. The Milky Way contains 200 billion stars.

Our galaxy moving within a local cluster of galaxies. Each one contains hundreds of billions of suns much like ours.

Are you starting to get the picture? There is no such thing as standing still.

When you describe how an object is moving, it is always in relation to where you are. Our falling ball, for example, can have its motion described in a variety of ways:

Description

1. The ball falls straight down.

2. The ball follows a parabolic path.

3. The ball moves mostly in a large circle.

4. The ball moves in a larger circle, and loops.

5. The ball moves through interstellar space in looping circles.

6. The ball moves in a huge drifting circle, with tiny loops every year, around the galaxy.
Frame of Reference:

... as seen from within the car.

... as seen by someone standing still on the surface of the earth.

... as seen by someone stationary in space above the earth.

... as seen by someone stationary above the solar system.

... as seen by someone stationary far from the solar system.

... as seen by someone stationary above the galaxy.

... and so on ...


Every one of these frames of reference is equally valid, and since nothing is ever truly 'at rest', there is no reason why the frame of reference on the surface of the earth ('the ball follows a parabolic path to the ground and stops') is any more correct than all the others. It's just more convenient, because mostly we spend all our time here.

When you are learning physics, expecially astrophysics, which deals with motions in a variety of different frames of reference, you have to make sure you specify which frame of reference you are talking about. And then you'll find out about light, which always appears to move at 300,000 km/s, regardless of what frame of reference you are in! In other words, if you are in a spacecraft moving at 99% of the speed of light, and shine a flashlight ahead of you, you will measure the speed of its light as still 300,000 km/s!!



Mr. Willis' Page