Answer to Question #26254 in Mechanics | Relativity for zameer

Question

(a) State against each observation below whether it is true or false. Give reasons for your answer.
i. The angular momentum of an artificial satellite rotating about the earth under its gravitation
varies with time
ii. An alpha particle scattered from an atomic nucleus moves in a plane.
iii. An artificial satellite moves at greater speed when it is nearer the earth. (6)
(b) When is the earth’s orbital motion around the sun fastest and when is it slowest? In which month
of the year is the earth closest to the sun? Explain in not more than 50 words. (4)

Answer 1

i. False
The only force acting on a satellite is gravitation. Momentof the force of gravity relative to the Earth is equal to zero, so angular
moment doesn't change.
ii. True
Two particles always move in a plane.
iii. True
According to the energy conservation law
Ep+Ek=const
-GMm/R+mv^2/2=const, where G - gravitationalconstant, m - satellite's mass, M - Earth's mass, R - distance from Earth to
satellite, v - satellite's velocity.
So, when R decreases v should increase. The same result canbe obtained using angular moment conservation law.
According to the iii, when Earth is nearest to the Sunvelocity is biggest, and when Earth is furthest it movement is slowest.
It is known that in January Earth is nearest to the Sun, soits movment is fastest, and in July Earth is furthest from the Sun, so it
movement is slowest