According to general relativity, the curvature of space-time caused by the mass of the Earth expands the horizon and the visible distance over the horizon. 

Without general relativity and space-time curvature, the visible distance over the horizon depends only on the radius of the Earth. For the Earth, with a radius of about 6,371 km, the visible horizon without space-time curvature is about 3,091 km (2 x Earth's radius).

Taking into account general relativity and space-time curvature, the visible horizon is increased. Some key numbers:

• The sun has a mass of 2 x 1030 kg. 
• The Earth's mass is 6 x 1024 kg. 
• The gravitational constant G = 6.674 x 1011 N m2/kg2.

Using these, we can calculate the Schwarzchild radius of the sun and Earth, which determines the amount of curvature:

• Sun's Schwarzchild radius = 2GM/c2 = 3 km 
• Earth's Schwarzchild radius = 2GM/c2 = 9 mm 

This curvature increases the visible horizon to:

• For the sun: About 1.37 times the Schwarzchild radius = 4.1 km 
• For the Earth: Roughly 1.41 times the Schwarzchild radius = 12.7 km

So the increased visible distance over the horizon due to general relativity is:

12.7 km - 3,091 km = 9,608 km 

This is an increase of over 300% compared to the horizon distance without relativity.

In summary, general relativity significantly expands our visible horizon due to the curvature of space-time produced by massive bodies like the Earth. The increased visible distance over the horizon is crucial for applications like space-based observations,satellite communications, and space navigation.

Let me know if you have any other questions!
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