1. Using Vertex Groups with Data Transfer modifier
Assign all the vertices of the sphere to Vertex Group with value of 1 and scale the sphere to very small size.
Create a vertex group and add DataTransfer modifier to the landscape object.
Then in the modifier select the sphere as Source Object, enable Vertex Data using Vertex Group(s) and set Vertex Mapping to Projected Face Interpolated.
2. Using Vertex Groups with VertexWeightMix modifier and spherical blend texture.
Create a Vertex Group with a value of 1 on all vertices of the landscape object.
Then add VertexWeightMix modifier, in the modifier select created vertex group in Vertex Groups A and B, set Mix Mode to Difference and create a new Texture Mask with Use Channel set to Value.
Then open texture settings, change Type to Blend, in Colors enable Ramp, set interpolation between color stops to Constant and Blend Progression change to Spherical.
Change to Weight Paint mode and adjust the texture color ramp till you get desired result.
3. Weight Paint mode with Transferring Weights to active object.
May not be as precise as previous methods but quicker to setup.
Assign all the vertices of the sphere to Vertex Group with value of 1.
Then in object mode select the sphere and holding Shift button select landscape object and switch to Weight Paint mode.
While in Weight Paint mode create a Vertex Group and in Tools tab click Transfer Weights button, then in Operator panel change Data Type to Vertex Group(s) and Vertex Mapping to Projected Face Interpolated and adjust Max Distance to get desired result.