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1. Consider launching a spacecraft on a least-energy orbit to Mercury. That orbit is an
elliptical orbit with the Sun at the focus, and with Earth and Mercury at aphelion and
perihelion, respectively. Consider the orbits of Earth and Mercury circular.
(a) What is the semi-major
axis of the spacecraft's
orbit? (A plot would help)
(b) What is the eccentricity of this orbit?
(c) How long will it take the spacecraft to arrive at Mercury?
(d) The Earth orbits around the Sun at about 30 km/s. What is the launch speed (and
its direction with respect to Earth's orbital motion) fa!' this probe to follow the
least-energy orbit? (Hint: First, find the aphelion speed for the least-energy orbit,
and then correct for the Earth's motion).
2. An eclipsing binary has an orbital period of 2d22hrs, the duration
hI'S and totality lasts 4 hI'S.
of each eclipse is 18
(a) Find the stellar radii in terms of circular orbital radius (a)
(b) If spectroscopic data indicate a relative orbital speed of 200 km/s,
actual stellar radii (in km and solar radii)
3.
what are the
(a) How much more energy per centimeter squared is emitted by a star at 20,000 K than
one at 5000 K?
(b) What is the predominant color of each star in part a? Use the \\fien displacement
law and express your answer in wavelengths.
4. You average body temperature
is 37° Centigrade.
(a) What is this in absolute units (Kelvin)? What is the peak wavelength emitted by a
person with this temperature?
(b) In what region of the spectrum is this wavelength? Is this consistent with the fact
that humans do not appear to glow (optically) in the dark?
(c) Estimate the surface area of your body (in m2). You are welcome to make any
reasonable assumptions and approximations, but be sure to state what they are!
(d) Assuming your body radiates like a blackbody (OK within a factor of 2-3), estjmate
the total power L radiated by your body in Watts. How does this compare to the
power requirement for a typical light bulb?
5. Consider two stars.
Inagnitude 4.
The first has apparent
magnitude
3, while the second has apparent,
(b) Assume the stars are so close together that we cannot distinguish them from one
another. Therefore, when we try to measure their brightness we are really measuring
their combined brightness. What is the combined apparent rnagnitude of the two
stars?
(c) Now assume the stars had apparent magnitude 7 and 8 and repeat the first part of
this problem (i.e. Now, how much brighter/dimmer is the first star than the second?)