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Exoplanet An exoplanet or extrasolar planet is a planet that orbits a star other than the Sun. Over 2000 exoplanets have been discovered since 1988....

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1. Exoplanet
An exoplanet or extrasolar planet is a planet that orbits a star other than the Sun. Over 2000 exoplanets
have been discovered since 1988. Specifically, 2098 planets in 1342 planetary systems including 509
multiple planetary systems as of 24 March 2016.
Exoplanets are usually found using very powerful telescopes. However, amateur astronomers can locate
some exoplanets using less powerful telescopes. Using these instruments produces small errors that
can affect the results of the observation, causing the exoplanet to look less bright. When the exoplanet
is viewed through a lens, the error E in magnitude ( brightness) is estimated by the following formula:
E(D, Z, h, T) = 0.09D-273 (27)-1/2(_1
1.75
cos Z
e(-h/8000)
Where D is the diameter, measured in cm, of the lens of the telescope; Z is the zenith angle, in degrees
of the planet, h is the altitude, in meters of the telescope, and T is the exposure time in seconds. The
zenith angle is defined to the angle from the highest point in the sky (Z=0') to an object in the sky.
1.
Suppose the diameter of the lens is 7.1 cm, the zenith angle is 20 and the altitude is 3000m,
what is the minimum exposure time needed to keep the error (E), below 0.001? Round to the
nearest second
2. Repeat Problem 1 for h = 4000m and h = 5000m. Comment on the effect of altitude on the error
3. Find lim E(7.1, Z,3000,180) and lim E(7.1, Z,3000,180) , Comment on the effect of the
z-0
z-,90
zenith angle on the error.
4. Find
OE
JE JE JE
aD ' oz ' oh ' OT
Interpret what these partials represent
5. Find the total differential dE ( what does this represent?)
6. Suppose D=7.1, Z = 20, h =3000, T = 180, use the total differential to determine which of the
following reduces the error by a greater amount:
a) Using a telescope with a lens diameter of 7.3 cm
b) Using a platform to increase the altitude of the telescope to 3200m

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