Estimating Time to Record Faint Star on Telescopes

[joker_900]

Homework Statement

An earth-based telescope with a mirror of diameter 2.4 m can record the im-
age of a faint star in 1 hour. A telescope placed in space (above the atmosphere)
has a mirror of the same focal length as that of the earth-based instrument, but
its diameter is 1.2 m. Atmospheric turbulence is assumed to place a limit of 0.25
seconds of arc on the angular resolution obtainable by earth-bound telescopes,
and the mean wavelength of the radiation detected is 550 nm. Estimate the
time required by the telescope placed in space to record the same star.

Homework Equations

f no. = focal length/aperture diameter

The Attempt at a Solution

The only thing I can think of is to calculate the f no. (focal length/mirror diameter) for each and say this is proportional to the time (as it is a measure of brightness, and so flux, and the greater the flux the shorter the time). However this would ignore any atmospheric effect of reducing flux.

There is another part to the question, so this part might not need all the information provided.

Thanks

 

[mgb_phys]

That's not a meaningful question.
The resolution doesn't determine the limiting magnitude (assuming an appropriately matched detector) the only effect putting it in space would have is to to remove sky background (which you aren't given) or atmospheric absorption.

 

[joker_900]

That's not a meaningful question.
The resolution doesn't determine the limiting magnitude (assuming an appropriately matched detector) the only effect putting it in space would have is to to remove sky background (which you aren't given) or atmospheric absorption.

Thanks for replying

There is a second part to the question which may be what the resolution information is for. But how would you go about this first part? What information would I need to determine the affect of the atmosphere on the brightness?

Thanks

 

[mgb_phys]

Sorry probably over analysing the question!
The signal received is proportional to the area of the mirror (assuming everything else is the same), so with half the mirror diameter it will have 0.25 the mirror area and a signal rate 4x less.

It's a common mistake from amateur astronomers that the limiting magnitude depends on the f# which is what I thought the question was asking. Although this is true for naked eye observing it isn't true for cameras.