The formula for gravitational force is given by:
F = (G * m1 * m2) / r^2
where:
F = gravitational force
G = gravitational constant (6.67430 x 10^-11 N(m/kg)^2)
m1 = mass of the Sun (1.99 x 10^30 kg)
m2 = mass of Jupiter (1.90 x 10^27 kg)
r = distance between the Sun and Jupiter (7.78 x 10^11 m)
Plugging in the values:
F = (6.67430 x 10^-11 N(m/kg)^2 * (1.99 x 10^30 kg) * (1.90 x 10^27 kg)) / (7.78 x 10^11 m)^2
F = (6.67430 x 10^-11 N(m/kg)^2 * 3.781 x 10^57 kg^2) / 6.0484 x 10^23 m^2
F = 25.231 x 10^46 N / 6.0484 x 10^23
F = 4.17 x 10^23 N
So, the average gravitational force between the Sun and Jupiter is approximately 4.17 x 10^23N.
Therefore, the correct answer is: 1. 4.17x10^23N
Answer:
1) [tex]4.17 \times 10^{23} \, \textsf{N}[/tex]
Explanation:
To calculate the average gravitational force between the Sun and the planet Jupiter, we can use Newton's law of universal gravitation:
[tex] F = \dfrac{{G \cdot m_1 \cdot m_2}}{{r^2}} [/tex]
Where:
[tex] F [/tex] is the gravitational force,
Given:
Substitute the given values into the formula:
[tex] F = \dfrac{{6.67 \times 10^{-11} \times (1.99 \times 10^{30}) \times (1.90 \times 10^{27})}}{{(7.78 \times 10^{11})^2}} [/tex]
[tex] F = \dfrac{{6.67 \times 1.99 \times 1.90 \times 10^{30+27-11}}}{{7.78^2 \times 10^{22}}} [/tex]
[tex] F = \dfrac{{6.67 \times 1.99 \times 1.90}}{{7.78^2}} \times 10^{46-22} [/tex]
[tex] F = \dfrac{{6.67 \times 1.99 \times 1.90}}{{7.78^2}} \times 10^{24} [/tex]
[tex] F = \dfrac{{25.21927}}{{60.5284}} \times 10^{24} [/tex]
[tex] F \approx 0.4166518527 \times 10^{24} \, \textsf{N} [/tex]
[tex] F \approx 4.166518527 \times 10^{23} \, \textsf{N} [/tex]
[tex] F \approx 4.17 \times 10^{23} \, \textsf{N} [/tex]
Therefore, the average gravitational force between the Sun and Jupiter is approximately [tex]4.17 \times 10^{23} \, \textsf{N}[/tex].
