[Mark Som (OP)]

How big would a satellite need to be in Low earth orbit (approx 250 miles) to appear to be the size of a postage stamp to the naked eye ?

[alancalverd]

Depends on the altitude of the postage stamp.

[Janus]

How big would a sattelite need to be in Low earth orbit (approx 250 miles) to appear to be the size of a postage stamp to the naked eye ?

As big as a postage stamp at what distance from the eye?  For example, the Full moon is about the "same size" as a quarter seen from a distance of 9 ft.   A quarter three feet away will appear to be 3 times wider than a full Moon.
Thus if you are considering a postage stamp held at arm's length (30" or 2.5 feet) and a standard postage stamp is 0.87x0.98 inch in size, then at 250 miles, the satellite would need to be about 7 1/2 x 8 miles in size to appear to be the same size.

[Petrochemicals]

Isn't there a rule someone knows about, such as," twice as large four times as close"

[Bored chemist]

Isn't there a rule someone knows about, such as," twice as large four times as close"

No.

[evan_au]

" twice as large four times as close"

It depends whether "large" is measuring width or area.

If "large" is measuring width: twice as wide = half the distance
If "large" is measuring area: four times the area = half the distance

[Bored chemist]

It depends whether "large" is measuring width or area.

No, it's just wrong.
Twice as large by area is 1.4142... times as close
Twice as large by a linear measure is twice as close.

Isn't there a rule someone knows about, such as," twice as large four times as close"

is wrong either way.

At any given distance a satellite the size of a postage stamp looks the same size as a postage stamp at the same distance.
The angle it will subtend at the eye will be the same as the postage stamp if the ratio of the distances is the same as the ratio of the sizes.

[Petrochemicals]

" twice as large four times as close"

It depends whether "large" is measuring width or area.

If "large" is measuring width: twice as wide = half the distance
If "large" is measuring area: four times the area = half the distance

I believe Evan its done by linear measurement in telescope camera circles. I cannot remember the specifications to look out for, I think the op could do that. Something to do with the human eye or hawk's eye being different, the lens presented in front of it etcetc gives you the amount of magnification.

[alancalverd]

"N times as close" is meaningless. We measure distance  (miles or microns)  to an object, not closeness ("per millimeter" applies to several packed objects, not one).

[Petrochemicals]

http://minerva.union.edu/malekis/CVision2003/MainPage/Course%20Content/Optics%20of%20Eye/OpticsofEye.htm

Maybe of interest