Question

1. Calculate the perihelion and aphelion speeds of the asteroid Toutatis, whose semimajor axis is 2.5321 AU and eccentricity 0.6288. Also calculate its period and note any relationship to that of Jupiter (again, this is easiest in AU using the simple form of Kepler’s third law).

Answer 1

Given

a=2.5321 Au

e=0.6288

The perihelion distance ,P=a(1-e)

P=2.5321(1-0.6288)

P=0.93991552 Au

Aphelion distance A=a(1+e)

A=2.5321(1+0.6288)

A=4.12428448 Au

According to kepler's law

T²=a³

T=a^3/2

T=2.5321^3/2

Period T=4.029 years

Semi major axis of jupiter ,a_jupiter=5.2044 Au

T²/a³=T²_jupiter/a³_jupiter

T_jupiter=(a_jupiter/a)^3/2 T

T_jupite=(2.5321/5.2044)^3/2 T

T_jupiter=0.3394 T