Question

what is the velocity of Pluto on elliptical and circular orbit. calculate it and compare it

Answer 1

Accoring to the concept of the gravitation

velocity of the elliptical orbit Ve={GM(2/r-1/a)}^1/2

the velocity of the circular orbit Vr={GM/r)^1/2

Given that

mass of the sun M=1.989*10^30 kg

gravitational constant G=6.67*10^-11 N.m^2/kg^2

distance b/w sun to pluto r=150*10^9 m

semi major axis [a=39.5 AU=59.1*10^11 m]

now we find the velocity of the circular orbit

velocity Vc=(6.67*10^-11*1.989*10^30/150*10^9}^1/2=2.974*10^4 m/s

now we find the velocity of the elliptical orbit

Ve={6.67*10^-11*1.989*10^30[(2/150*10^9)-(1/59.1*10^11)}^1/2

={6.67*1.989*10^19[1.33*10^-11-0.02*10^-11]}^1/2

=4.2*10^4/2.974*10^4=1.41

Ve=1.41Vc

Ve/Vc=4.2*10^4/