# Why aren't satellites increasing speed because of gravitational acceleration?

Satellites orbiting the earth are experiencing almost as strong gravitation as we do, but they don't hit the earth because of their velocity outwards and the earth's curvature. But if they're accelerating at 9,81m/s2 (actually slightly less), wouldn't the speed increase be ridiculously high after a while? I'm sure I've misunderstood something obvious here, but I couldn't find an explanation for this anywhere so I needed to get this off my mind.

• Hint: What is the angle between velocity and acceleration for an orbiting object? Apr 16, 2015 at 20:57
• If the acceleration were always in one direction, the speed would increase. But because it is not always in one direction, the summation cancels out to zero net change. Apr 16, 2015 at 21:01
• They sort of do... but then they end up going so fast that they "overshoot" the planet, and go higher up, where they move slower, so gravity has more time to pull them down, so they move faster, so they overshoot the planet, etc... (In other words: a satellite in a non-perfectly-circular orbit will have an oscillating speed). Ever played Kerbal Space Program? Apr 17, 2015 at 7:01
• If you remember how to add vectors then this tool can visualize it for you (Check boxes in "Newtonian features" tab on bottom to visualize vectors)
– PTwr
Apr 17, 2015 at 7:04

For simplicity, consider a perfectly circular orbit; the gravitational acceleration is always at a right angle to the velocity vector.

This means that the speed cannot change despite the fact that there is constant acceleration.

Note that for the speed to change, there must be a non-zero component of acceleration parallel (or anti-parallel) to the velocity vector. If the acceleration is always perpendicular, only the direction of the velocity will change, not the magnitude (speed).

For an elliptical orbit, the speed does change but the change is periodic; increasing to a maximum and then decreasing to a minimum at regular intervals.

• And obvious it was... Thanks Alfred and everybody else for answering my question in less than 15 minutes! Apr 16, 2015 at 21:05

Acceleration is any change in velocity, whether it's the direction of the velocity or its magnitude. In the case of a perfect orbit it is the direction, the tangential velocity of the satellite should keep a constant magnitude and just change direction as the satellite orbits.

When the velocity is slightly less than what is needed for a perfect orbit, it usually results in an elliptical orbit, in which the magnitude of the tangential velocity also changes. As the satellite gets closer to Earth, it's speed increases, which causes it to be launched farther away from the Earth which then results in it slowing down and repeating the cycle. Assuming there is nothing to interrupt this cycle, the satellite can remain in such an orbit indefinitely.
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