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I've had a kerbal in a decaying orbit for some time now (I lose about a meter to my apoapsis every 3 seconds), with an apopsis of ~80km and periapsis of ~67 km. I've made a few rotations around Kerbal, but my 'Achieve orbit' contract has not gained a check-mark. My orbit has since decayed, as seen below, and I expect I will not complete the contract despite several successful rotations around Kerbal.

enter image description here

Am I failing to meet some hidden criteria? What are the exact criteria needed to complete this contract?

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After re-reading the contract from the Contracts screen, I see that there is a minimum periapsis of 70 km. So close!

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    Yep, if your periapsis isn't above 70km (for Kerbin), your orbit isn't stable, at least according to the game. Also, I think you need to stage in order for the contract to be fulfilled. – MBraedley Dec 14 '14 at 3:09

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