Download A new picture of Halley`s Comet [Translated and adapted from

A new picture of Halley’s Comet
[Translated and adapted from Sterne und Weltraum, 11/03]
This picture of the nucleus of Halley’s Comet [the dark smudge at the centre] was taken in
March this year. At the time it was 27⋅26 Astronomical Units [AU] from the Earth and 28⋅06
AU from the Sun, the furthest that a comet has ever been photographed. The 5km × 5km ×
15km nucleus, is currently about a thousand million times fainter than the faintest star that
can be seen with the naked eye.
The picture was taken using three of the four 8⋅2 m diameter telescopes of the European
Space Agency’s Very Large Telescope (VLT), which gathered the light from Halley for 3
nights. Altogether 81 pictures were taken, each by a single scope, with a total exposure time
of 32 284 seconds. The pictures were added together electronically and the images of stars
subtracted to give the image above.
At the very low brightness of Halley, only one photon every 1⋅6 seconds was received - a
total of about 20 000 photons.
The cometary nucleus has now travelled about four fifths of its way to its perihelion [the
furthest distance from the Sun] of about 35 AU, which it will reach in December 2023. The
comet will return to the inner Solar System in 2061.
The questions investigate the figure given for the number of photons from Halley, which were
received by the VLT scopes.
1.
2.
3.
4.
5.
6.
7.
8.
The Solar Constant, the light flux from the Sun at the distance of the Earth [150 million
km, or 1 AU], is 1⋅37 kW m-2. Use this figure to calculate the power output of the Sun.
Calculate the mass loss of the Sun per second represented by the power output you
calculated in question 1. [Hint: E = m c2]
Show that the light flux at Halley’s Comet at a distance of 28⋅06 AU is approximately
2 W m-2.
Estimate the total solar power reaching Halley’s Comet. [You will need to make an
assumption about how the nucleus is oriented.]
If the mean photon energy of the Solar radiation is 2⋅5 eV, estimate the number of solar
photons hitting Halley each second.
Halley’s nucleus is darker than soot! The current measurement of its albedo, that is the
fraction of the incident radiation which is reflected, is 0⋅027. Estimate the flux of
photons from Halley’s comet each second which reach the Earth [i.e. the number of
photons per m2 per second].
For an 8⋅2 m diameter telescope find the mean time between the arrival of photons.
If another image is taken in 2023, what will the time interval between the photons’
arrival be?
Gareth Kelly
02 November 2003