Environmental Engineering Reference
In-Depth Information
If the star emits a short burst of radiation which drives away the dust cloud
but leaves the planet's position and velocity unchanged show that the planet
remains bound to the star if the initial radius is smaller than
(
3
M/(
4
πρ))
1
/
3
.
Determine the semi-major axis, eccentricity and period of the new orbit.
9.6 In Example 9.5.3, we investigated the motion of the Apollo 11 spacecraft as
it orbited the Moon. The astronauts boarded the Eagle lunar module in order
to descend to the Moon's surface. The Eagle detached from the command
module when the spacecraft was at a height of 110 km above the Moon's sur-
face and immediately fired its rockets to reduce its speed so that it transferred
into an elliptical orbit with a perigee of 15 km above the Moon's surface. By
how much did the lunar module need to reduce its speed in order to shift to
this orbit? [The radius of the Moon is 1740 km.]
9.7 The Earth's orbit about the Sun has an eccentricity of 0.017 and mid-winter
in the northern hemisphere occurs when the Earth is close to perihelion. Use
this information in conjunction with Kepler's Second Law to estimate by how
many days summer is longer than winter in the northern hemisphere. Compare
your answer to that which you would get by counting the days between the
relevant equinoxes.
