IB Physics Topic D.1.1 Laws and Properties of Gravitational Fields Revision Notes (SL/HL)

IB Physics Topic D.1.1 Laws and Properties of Gravitational Fields Revision Notes (SL/HL) | RevisionDojo

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The Universal Law of Gravitation

Newton's law of gravitation describes the attractive force between any two objects with mass.
The force is given by: $$F = G \frac{m_1 m_2}{r^2}$$ where:
1. $F$ is the gravitational force between the masses (in newtons, N).
2. $G$ is the universal gravitational constant, approximately $6.67 \times 10^{-11} \, \text{N m}^2 \ \text{kg}^{-2}$.
3. $m_1$ and $m_2$ are the masses of the two objects (in kilograms, kg).
4. $r$ the distance between the centers of the two masses (in meters, m).

Note

The gravitational force is always attractive and acts along the line joining the two masses.

Application to Spherical Masses

Newton proved that for spherical bodies with uniform density, the gravitational force can be calculated as if all the mass were concentrated at the center of the sphere.

This simplifies calculations for planets, stars, and other spherical objects.

Example question

Calculate the gravitational force between Earth and the Moon, given:

Mass of Earth: $m_1 = 5.97 \times 10^{24} \, \text{kg}$
Mass of Moon: $m_2 = 7.35 \times 10^{22} \, \text{kg}$
Distance between centers: $r = 3.84 \times 10^8 \, \text{m}$

Solution

Substitute the given values into the formula:

$$F = G \frac{m_1 m_2}{r^2} = (6.67 \times 10^{-11}) \frac{(5.97 \times 10^{24})(7.35 \times 10^{22})}{(3.84 \times 10^8)^2}$$

$$F \approx 1.98 \times 10^{20} \, \text{N}$$

This is the gravitational force between Earth and the Moon.

Conditions for Point Mass Approximation

Newton’s law of gravitation is derived for point masses, but it can be applied to extended bodies under certain conditions:

Spherical Symmetry: The body must be spherical and have a uniform mass distribution.
Distance: The distance between the bodies must be much larger than their sizes.

Tip

For non-spherical bodies, the gravitational force can be complex.
However, if the body is far enough away, it can often be approximated as a point mass.

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The Universal Law of Gravitation

Newton's law of gravitation describes the attractive force between any two objects with mass.
The force is given by: $$F = G \frac{m_1 m_2}{r^2}$$ where:
1. $F$ is the gravitational force between the masses (in newtons, N).
2. $G$ is the universal gravitational constant, approximately $6.67 \times 10^{-11} \, \text{N m}^2 \ \text{kg}^{-2}$.
3. $m_1$ and $m_2$ are the masses of the two objects (in kilograms, kg).
4. $r$ the distance between the centers of the two masses (in meters, m).

Note

The gravitational force is always attractive and acts along the line joining the two masses.

Application to Spherical Masses

Newton proved that for spherical bodies with uniform density, the gravitational force can be calculated as if all the mass were concentrated at the center of the sphere.

This simplifies calculations for planets, stars, and other spherical objects.

Example question

Calculate the gravitational force between Earth and the Moon, given:

Mass of Earth: $m_1 = 5.97 \times 10^{24} \, \text{kg}$
Mass of Moon: $m_2 = 7.35 \times 10^{22} \, \text{kg}$
Distance between centers: $r = 3.84 \times 10^8 \, \text{m}$

Solution

Substitute the given values into the formula:

$$F = G \frac{m_1 m_2}{r^2} = (6.67 \times 10^{-11}) \frac{(5.97 \times 10^{24})(7.35 \times 10^{22})}{(3.84 \times 10^8)^2}$$

$$F \approx 1.98 \times 10^{20} \, \text{N}$$

This is the gravitational force between Earth and the Moon.

Conditions for Point Mass Approximation

Newton’s law of gravitation is derived for point masses, but it can be applied to extended bodies under certain conditions:

Spherical Symmetry: The body must be spherical and have a uniform mass distribution.
Distance: The distance between the bodies must be much larger than their sizes.

Tip

For non-spherical bodies, the gravitational force can be complex.
However, if the body is far enough away, it can often be approximated as a point mass.

Definition

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(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Duis aute irure dolor in reprehenderit

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Excepteur sint occaecat cupidatat non proident

Tip

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics D.1.1 Laws and Properties of Gravitational Fields Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

The Universal Law of Gravitation

Application to Spherical Masses

Conditions for Point Mass Approximation

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The Universal Law of Gravitation

Application to Spherical Masses

Conditions for Point Mass Approximation

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Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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