**ASTR430 HW#2 (due 10/12/05)**

- Transfer orbits.
- Do problem #20 from Ch. 3 in the textbook (p. 73), assuming
the orbits of Phobos and Deimos are circular and co-planar.
Neglect the mass and finite size of the moons. Include a sketch
of the situation showing Mars, Phobos, Deimos, and the desired
orbit. This is an example of a Hohmann transfer orbit.
- What is the eccentricity of the transfer orbit?
- What is the minimum time required for the package to get from
Phobos to Deimos?
- At what relative orbital longitudes will the moons need to be
at launch for Deimos to be at the correction position when the
package arrives? How often does this configuration occur (in
other words, what is the
*synodic*period of Deimos relative to Phobos)?

- Do problem #20 from Ch. 3 in the textbook (p. 73), assuming
the orbits of Phobos and Deimos are circular and co-planar.
Neglect the mass and finite size of the moons. Include a sketch
of the situation showing Mars, Phobos, Deimos, and the desired
orbit. This is an example of a Hohmann transfer orbit.
- Gravitational potential energy.
- Derive an expression for the gravitational potential energy of
a homogeneous sphere of bulk density , mass , and radius
.
*Hint:*consider the contributions of thin concentric shells of thickness and mass .

- Derive an expression for the gravitational potential energy of
a homogeneous sphere of bulk density , mass , and radius
.
- Gravitational collapse.
- Derive a formula for the free-fall gravitational collapse time
of a uniform spherical cloud of density .
*Hint:*the trajectory of a gas parcel initially at rest at a distance from the center of the cloud can be approximated as a very eccentric ellipse with semimajor axis . - Calculate the collapse time for a cloud of H molecules
with molecules per cubic centimeter.
- Do problems #21 & 22 from Ch. 4 in the textbook (p. 97).

- Derive a formula for the free-fall gravitational collapse time
of a uniform spherical cloud of density .
- Planetesimal accretion.
- Do problems #14 & 15 from Ch. 5 in the textbook (p. 125).
For #14, assume the planetesimal is on a straight-line trajectory
with speed relative to the cloud, and ignore gravitational
focusing.

- Do problems #14 & 15 from Ch. 5 in the textbook (p. 125).
For #14, assume the planetesimal is on a straight-line trajectory
with speed relative to the cloud, and ignore gravitational
focusing.