Download Astronomy 340 Fall 2005

Astronomy 340 Fall 2005
Homework #1
Due Sep 27 at the beginning of class.
Problem 1. The perihelion distance of an orbiting body is 2.3 AU. When it has traveled
an angular distance of 60 degrees its distance from the Sun is 3.0AU. What are its semimajor axis and eccentricity?
Problem 2. An asteroid moving in the ecliptic is seen with coordinates x = 1.2 AU and y
= 0.8 AU moving along a direction making a counter-clockwise angle of 55 degrees with
the x-axis speed of 20 km s-1. What are the semi-major axis and eccentricity of its orbit?
Is it an Earth-crossing asteroid?
Problem 3. Problem 2.2 in Planetary Sciences.
Problem 4. Derive an expression for the velocity of a planet at an arbitrary point in its
orbit. Based on your derivation, what are the minimum and maximum orbital velocities
for the nine planets?
Problem 5. As we briefly discussed in class, tidal forces between the Earth and the
Moon are pushing the Moon’s orbit away from the Earth and slowing down the Earth’s
spin.
a) Calculate the Earth’s spin angular momentum, the Moon’s spin angular
momentum, and the Moon’s orbital angular momentum. Assume the angular
momentum vectors are aligned and that the lunar orbit is perfectly circular.
b) Assume that only tidal forces between the Earth and the Moon are operating and
argue that the total angular momentum of the Earth-Moon system is conserved. Is
the orbital energy conserved? Explain your reasoning.
c) In the end state of orbital evolution, the Moon will be further away from the Earth
and the Earth will always keep one face toward the Moon. That is, the month will
be the same as the day. Use conservation of angular momentum to determine
how far the Moon will be from the Earth and how long the “day” will be. You
can neglect the spin angular momentum of the Moon. The final equation cannot
be solved analytically; try to get a solution with a numerical or graphical method.
Problem 6. Problem 2.19 in Planetary Sciences
Problem 7. Problem 2.20 in Planetary Sciences
Problem 8. Taking into account the eccentricities of the Moon’s orbit around the Earth
(0.056) and the Earth’s orbit around the Sun (0.017) find the ratio of the maximum to the
minimum tidal forces at the Earth’s surface.