umkreisen
to orbit
To move along a circular or elliptical path around a central point or body.
Der Mond umkreist die Erde in etwa 27 Tagen.
The Moon orbits the Earth in about 27 days.

to orbit / circle
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to orbit
To move along a circular or elliptical path around a central point or body.
Der Mond umkreist die Erde in etwa 27 Tagen.
The Moon orbits the Earth in about 27 days.

'Umkreisen' consists of the prefix 'um-' (around) and the verb 'kreisen' (to circle). The prefix is inseparable, which means it always stays at the beginning of the verb, even in a main clause.
Ein Satellit umkreist die Erde in 90 Minuten.
A satellite orbits the Earth in 90 minutes.
Because 'umkreisen' is an inseparable verb, the past participle is formed without the prefix 'ge-'. The correct form is 'hat umkreist' (has orbited/circled), not 'hat umgekreist'.
Die Raumsonde hat den Planeten Jupiter erfolgreich umkreist.
The space probe successfully orbited the planet Jupiter.
The verb 'umkreisen' always requires a direct object in the accusative. You ask: Whom or what does someone or something circle/orbit?
Die Wölfe umkreisten ihre Beute langsam.
The wolves slowly circled their prey.
Besides literal movement, 'umkreisen' can also be used figuratively for thoughts or topics. When thoughts 'ein Problem umkreisen' (circle around a problem), you are constantly occupied with it.
Seine Gedanken umkreisten immer wieder dieselbe ungelöste Frage.
His thoughts kept circling around the same unresolved question.
to surround
'umgeben' and 'umkreisen' both have to do with movement or position around something. The important difference is: 'umgeben' usually describes a state. Something is located all around a person or thing. 'umkreisen', on the other hand, describes movement in a circle or repeatedly around something. The words can be confused because both contain the image of 'around something'. So pay attention to the question: Is something standing or lying all around? Then 'umgeben' fits. Is something moving around it? Then 'umkreisen' fits.

Mehrere Möwen umkreisen das Fischerboot.
Several seagulls circle the fishing boat.
Blumen umgeben den Brunnen in der Mitte des Parks.
Flowers surround the fountain in the middle of the park.