How do shifts in earth's orbit affect the global climate?

The earth's orbit is an ellipse with the sun in one of its foci. This orbit is affected by some variations that impact on the climate following what are called "Milankovitch Cycles" from the name of the Serbian astronomer who calculated the magnitude of such variations.

Eccentricity: the orbit of the earth varies its eccentricity between 0 and 5% in a cycle of about 100,000 years. These variations change the distance between earth and sun thus changing the amount of solar energy reaching the planet during the different seasons. More eccentricity means stronger difference between summer and winter.

Axial tilt: the inclination of the Earth's axis in relation to the plane of the orbit changes with a cycle of 41,000 years from 21.5 to 25.5 degree. A smaller tilt will lead to more snow in winter in the polar regions and less warm summer promoting the grow of ice caps leading to glaciation.

Precession: the Earth's axis wobbles with a cycle of 23,00 years. This precession affects the contrast between summer and winter.

The overall impact of these cycles is a periodical return of ice ages followed by inter-glacial periods.

Long-term warming or cooling of the planet's temperature can result from variations in the amount and distribution of solar radiation that reaches Earth due to shifts in the Earth's orbit.