Question

t some moment, two giant planets jupiter and saturn of the solar system are in the same line as seen from the earth. Find the total gravitational force due to them on a person of mass 50 kg on the earth. Could the force due to the planets be important?
Mass of the jupiter = 2 x 1027 kg
Mass of the saturn = 6 x 1026 kg
Distance of jupiter from the earth
= 6.3x 1011 m
Distance of saturn from the earth
= 1.28 x 1012m
Gravitational constant,
G = 6.67 x 10-11N -m2 /kg2
Acceleration due to gravity on the earth
=9.8 m/s2

Answer 1

Answer:

96.30005

Explanation:

Answer 2

Complete Question: At some moment, two giant planets Jupiter and Saturn of the solar system are in the same line as seen from the Earth. Find the total gravitational force due to them on a person of mass 50 kg on the earth. Could the force due to the planets be important?

Mass of the Jupiter = 2 × 10²⁷ kg

Mass of the Saturn = 6 × 10²⁶ kg

Distance of Jupiter from the earth = 6.3 × 10¹¹ m

Distance of Saturn from the earth = 1.28 × 10¹² m

Gravitational constant (G) = 6.67 × 10⁻¹¹ N m² kg⁻²

Acceleration due to gravity on the earth (g) = 9.8 ms⁻²

→ Answer: The total gravitational force on the person due to Saturn and Jupiter is equal to 1.8 ×10⁻⁵ Newton.

The forces due to these planets are not important because the force of attraction between the person and the Earth is much greater than the force of attraction due to these two planets.

Given:

Mass of Jupiter (m₁) = 2 × 10²⁷ kg

Mass of Saturn (m₂) = 6 × 10²⁶ kg

Distance of Jupiter from Earth (d₁) = 6.3 × 10¹¹ m

Distance of Saturn from Earth (d₂) = 1.28 × 10¹² m

Gravitational Constant (G) = 6.67 × 10⁻¹¹ N m² kg⁻²

Mass of the person (m) = 50 kg

Acceleration due to gravity on Earth (g) = 9.8 ms⁻²

To Find:

The total gravitational force (F) due to the two planets on a person of mass 50 kg on Earth.

Solution:

According to Newton's laws of gravitation:

• The force of attraction between two objects acts along the line joining their centers.

• The force of attraction between two objects is directly proportional to the product of their masses (m₁m₂) and inversely proportional to the square of the distance (d) between their centers of mass.
• The formula for the gravitational force of attraction (F) between two bodies is given as:

                                          $F=G\frac{m_{1} m_{2} }{d^{2} }$

→ The force of attraction (F₁) between Jupiter and the person on Earth:

                     $\therefore F_{1} (Force\:due \:to\:Jupiter)=G\frac{(m_{1})( m)}{(d_{1})^{2} }$

                        $F_{1} =(6.67 \times10^{-11} )\times\frac{(2 \times 10^{27} )\times (50) }{(6.3\times10^{11} )^{2} } \\\\F_{1} =1.68 \times 10^{-5} N$

→ The force of attraction (F₂) between Saturn and the person on Earth:

                     $\therefore F_{2} (Force\:due \:to\:Saturn)=G\frac{(m_{2})( m)}{(d_{2})^{2} }$

                        $F_{2} =(6.67 \times10^{-11} )\times\frac{(6 \times 10^{26} )\times (50) }{(1.28\times10^{12} )^{2} } \\\\F_{2} =1.22 \times 10^{-6} N$

→ Since in the given question, Jupiter and Saturn are in the same line therefore the force of attraction due to these two planets on the person on Earth would be along the same straight line.

→ Hence the force of attraction due to Jupiter (F₁) and due to Saturn (F₂) on the person on Earth would get added up in order to calculate the Net force experienced by the person due to these two planets.

                     ∴ Total gravitational Force on Person (F) = F₁ + F₂

                     ∴ F = (1.68 × 10⁻⁵) + (1.22 × 10⁻⁶)

                     ∴ F = 1.8 ×10⁻⁵ Newton

Hence the total gravitational force on the person due to Saturn and Jupiter is equal to 1.8 ×10⁻⁵ Newton.

→ Force of attraction between the person and Earth = Weight of the person

∴ Force of attraction between the person and Earth =mg = 50 × 9.8 = 490N

The forces due to these planets are not important because the force of attraction between the person and the Earth (490 N) is much greater than the force of attraction due to these two planets (1.8 ×10⁻⁵ N).

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