You're looking for simple explanations,
but the explanation above is not simple at all.
Can you explain simply, what makes the Moon drift away from the Earth?
What about the objects which don't move toward mass? For example, the Moon does not move toward the Earth. Moreover, the Moon slowly drifts away from the Earth.
I'm sorry, I've just realized that my previous post appears to reply to @TheVat, which was not my intention. I repeat it here because I think @MasterOgon might be interested, as my daughter, an artist (albeit in a different genre and several years ago), used to like that site:
You are given four pieces of chain shown on the left, and you want to make a circular chain shown on the right. What is a minimum number of links you need to cut to do the job?
It cannot be a proper length because proper length has a meaning only between events which are spacelike related, i.e., nothing can get from one to another unless it moves faster than light.
Are you familiar with the Deviant Art community? I think you'd find many friends there:
DeviantArt - The Largest Online Art Gallery and Community
E.g., see this:
Search 'space art' on DeviantArt - Discover The Largest Online Art Gallery and Community
Or this:
Search 'sci-fi art' on DeviantArt - Discover The Largest Online Art Gallery and Community
Still doesn't work. If the body went 1 km in 1 s, the length of the geodesic is sqrt(300000^2-1) and divided by the coordinate time it gives the "speed" of about 300000 km/s.
This is incorrect because length of a geodesic path is proper time. So, your formula produces time over time rather than speed.
For example, if two events occur in the same place with 1 min one after another, the length of the geodesic path is 1 min and the "speed" according to your formula is 1/1 = 1.
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