Question

The force of gravity between the Sun and Jupiter is 5

Answer 1

ANSWER

1.8 x 10²⁷ kg

EXPLANATION

Given:

• The force of gravity between the Sun and Jupiter, F = 5x10²³N

,

• The mass of the Sun, m₁ = 2x10³⁰kg

,

• The distance between Jupiter and the Sun, r = 7x10¹¹m

Unknown:

• The mass of Jupiter, m₂

By Newton's Law of Universal Gravitation,

$F=G\cdot\frac{m_1m_2}{r^2}$

Where G is the gravitational constant, which has a value of approximately 6.67x10⁻¹¹m³/kg*s².

Solving this equation for m2,

$m_2=\frac{r^2\cdot F}{G\cdot m_1}$

Replace with the values and solve,

$m_2=\frac{(7\times10^{11}m)^2\cdot(5\times10^{23}N)}{(6.67\times10^{-11}\frac{m^3}{\operatorname{kg}\cdot s^2})\cdot(2\times10^{30}\operatorname{kg})}\approx1.8\times10^{27}\operatorname{kg}$

Hence, the mass of Jupiter is 1.8x 10²⁷ kg.