1.200. A planet of mass
M
moves along a circle around the Sun
with velocity v = 34.9 km/s (relative to the heliocentric reference
frame). Find the period of revolution of this planet around the Sun.
1.201. The Jupiter's period of revolution around the Sun is 12
times that of the Earth. Assuming the planetary orbits to be circular,
find:
(a)
how many times the distance between the Jupiter and the Sun
exceeds that between the Earth and the Sun;
(b)
the velocity and the acceleration of Jupiter in the heliocentric
reference frame.
1.202. A planet of mass
M
moves around the Sun along an ellipse
so that its minimum distance from the Sun is equal to
r
and the maxi-
mum distance to
R.
Making use of Kepler's laws, find its period of
revolution around the Sun.
1.203. A small body starts falling onto the Sun from a distance
equal to the radius of the Earth's orbit. The initial velocity of the
body is equal to zero in the heliocentric reference frame. Making
use of Kepler's laws, find how long the body will be falling.
1.204. Suppose we have made a model of the Solar system scaled
down in the ratio but of materials of the same mean density as
the actual materials of the planets and the Sun. How will the orbital
periods of revolution of planetary models change in this case?
1.205. A double star is a system of two stars moving around the
centre of inertia of the system due to gravitation. Find the distance
between the components of the double star, if its total mass equals
M
and the period of revolution
T.
1.206. Find the potential energy of the gravitational interaction
(a)
of two mass points of masses m
l
and m
2
located at a distance
r
from each other;
(b)
of a mass point of mass m and a thin uniform rod of mass
M
and length
1,
if they are located along a straight line at a distance a
from each other; also find the force of their interaction.
1.207. A planet of mass m moves along an ellipse around the Sun
so that its maximum and minimum distances from the Sun are equal
to r
1
and
r
2
respectively. Find the angular momentum
M
of this
planet relative to the centre of the Sun.
1.208. Using the conservation laws, demonstrate that the total
mechanical energy of a planet of mass m moving around the Sun
along an ellipse depends only on its semi-major axis a. Find this
energy as a function of a.
1.209. A planet A moves along an elliptical orbit around the Sun.
At the moment when it was at the distance r
0
from the Sun its velo-
city 'was equal to v
o
and the angle between the radius vector r
0
and
the velocity vector v
o
was equal to a. Find the maximum and mini-
mum distances that will separate this planet from the Sun during
its orbital motion.
1.210. A cosmic body
A
moves to the Sun with velocity v
o
(when
far from the Sun) and aiming parameter
1
the arm of the vector v
