A beautiful formula for what angle an object in space extends at you? Its the (diameter-of-object / distance -of-object) ratio is the tangent of that angle. Then, the farther the object is the smaller the angle becomes maintaining the tangent value of the angle in that ratio, because the object will have a fixed size/diameter.
δ = inverse-tan ( diameter / distance )
This formula then I will remember all my life. Give me Einstein Tensor and bet that I will remember you will lose that bet. I hear applauds, Thank you.
This image then shows the size of earth from the distance of the Rocket that has been sent by India recently. This formula and info is from ISRO fb page ( — although explanation is mine) and yes this is valid only for circular objects (earth on a plane is a near-circle, as you can see in the image above) and the circle on this square-image-space extends an angle with a point that is as far from the square as is the Rocket.
Just appending something from Jan 26, 2012 thats about 2 years ago almost when I was hooked up onto a similar problem and had drawn a schematic.
Sky is illusion. I looked at the sky just a while ago and I see a rocket is moving on the top of the moon. Now the star is also at the level of the moon. You say the very slight angle extended by star also means its hugely elevated to the moon, its so far away. What about the rocket, the moon is only 1 light-second away and thats a staggering 3,00,000 kms whereas the rocket is flying only on the earth.