Question

The mass of Jupiter is 1.9 × 1027 and that of the sun is 1.99 × 1030. The

mean distance of Jupiter from the sun is 7.8 × 1011m. Calculate the gravitational

force which the sun exerts on Jupiter, and the speed of Jupiter.​

Answer 1

F = 4.147 × 10^23

v = 1.31 × 10^4

Step-by-step explanation:

Given the following :

mass of Jupiter (m1) = 1.9 × 10^27

Mass of sun (m2) = 1.99 × 10^30

Distance between sun and jupiter (r) = 7.8 × 10^11m

Gravitational force (F) :

(Gm1m2) / r^2

Where ; G = 6.673×10^-11 ( Gravitational constant)

F = [(6.673×10^-11) × (1.9 × 10^27) × (1.99 × 10^30)] / (7.8 × 10^11)^2

F = [25.231 × 10^(-11+27+30)] / (60.84 × 10^22)

F = (25.231 × 10^46) / (60.84 × 10^22)

F = 3.235 × 10^(46 - 22)

F = 0.4147 × 10^24

F = 4.147 × 10^23

Speed of Jupiter (v) :

v = √(Fr) / m1

v = √[(4.147 × 10^23) × (7.8 × 10^11) / (1.9 × 10^27)

v = √32.3466 × 10^(23+11) / 1.9 × 10^27

v = √32.3466× 10^34 / 1.9 × 10^27

v = √17. 023 × 10^34-27

v = √17.023 × 10^7

v = 13047.221

v = 1.31 × 10^4