Herndon-based GeoEye has offered to pay $792 million in cash and stock for its Longmont, Colo.-based competitor DigitalGlobe at a time when the satellite-imagery business will likely be hit by federal belt-tightening.

The deal would give DigitalGlobe shareholders $17 per share of the company, a figure that includes $8.50 in cash and $8.50 in GeoEye stock. The price tag marks a 26 percent premium over the firm’s closing value on May 3.

In an open letter to Jeffrey Tarr, the president and chief executive of DigitalGlobe, GeoEye chief executive Matt O’Connell said the companies had discussed a potential merger “during the past few months” as a way to combine resources and survive budget cuts.

O’Connell explained in an interview that a combined company would be able to reduce capital expenses by constructing fewer satellites over time and requiring fewer ground stations. Both firms are in the midst of building satellites, and O’Connell said he did not expect those projects to be affected.

Calls to DigitalGlobe were not returned.

“It’s hard to make the argument that the companies are better off separate, and I think anyone in government would agree with that as well,” said Andrea James, an industry analyst with Minneapolis-based Dougherty & Co.

The proposal comes as both companies prepare for prospective cuts to a $7.3 billion contract called EnhancedView that was awarded in 2010 to provide satellite imagery to theNational Geospatial-Intelligence Agency.