Question

The average radius of orbit for Jupiter is 7.78 x 10^11 m. Using C = 3.355 x 10^18 m^3/s^2, the period of orbit for Jupiter is

Answer 1

Time period of a planet around sun(T) is given by

T=2r3/GM . Where r=avrage radius of orbit of planet G=gravitational constant, M=mass of sun

Therefore  T2=42r3/GM

r3=(GM/42)T2 . But (GM/42)=C= 3.355 x 1018 m3/s2 (given)

That is   r3=CT2

T2= r3/C . where r=avrage radius of orbit of Jupiter=7.78 x 1011m

T=[( 7.78 x 1011)3/3.355 x 1018 ] = ​​​​​​​[( 7.78 x 1011)3/33.55 x 1017 ]

=3.7x108sec