Gravitational Fields

Gravitational Fields

Shiken premium Upgrade Banner

Have you ever wondered why things fall back to the ground? Well, it's because of something called gravitational fields. Sir Isaac Newton, a famous physicist, discovered that anything that goes away from the earth gets pulled back towards it. So, if you throw a ball in the air, it doesn't matter which direction it goes, it will eventually fall back down to the ground. This even happens if you throw it really high!

To keep something from falling back to the ground, you need a lot of force. This is why planes need engines and lift from their wings to stay in the air. Without these forces, they would crash down to the earth.

What is gravity?

Gravity is a force that pulls all objects with mass towards each other. Since the earth has mass, it pulls other objects towards it. And, interestingly enough, we also attract the earth towards ourselves using gravity!

You might be wondering why we don't see objects attracting each other more often, given that everything has mass. Well, let's dive into that a bit more.

Gravity is not just a force but a force field

A force field is an area where objects can experience a force without any physical contact. This happens because force fields cause interactions between particles and objects, even if they're not touching each other. When it comes to gravity, this interaction occurs between objects that have mass. So, if you place any object within the gravitational field of another object, it will experience an attractive force towards that object.

The vector representation of force fields

Force fields can be represented as a system of vectors, as in this diagram, in which the arrows represent the gravitational field on the earth.

 Gravitational field lines
Gravitational field lines

The gravitational field of the Earth is radial in nature, which means that the lines of force intersect at the center of the Earth. The diagram also shows that the field lines are closer together at the Earth's surface, which indicates that the gravitational force is stronger in this region. On the other hand, where the lines move further apart from each other, the force decreases.

How do we calculate the force of gravity?

Have a look at the equation below, which represents Newton’s law of gravitation:

F = magnitude of the gravitational force.

G = gravitational constant.r = distance between the centres of two masses.= mass of one of the objects.= mass of the other object.

Newton’s gravitational field: when two bodies are placed in a gravitational field, they experience a force that is the product of the two masses and the inverse square of the distance from the centre of both masses.

The constant G is a gravitational constant, which has a very small value:

Calculate the gravitational force between two 3kg spheres that are 2m apart.

The mass of both objects is 3kg. So m1 and m2 are 3kg, while r is 2m, with G being 6.67 * 10 ^ -11 Nm ^ 2 / kg ^ 2. Putting in all the values gives us:

The gravitational constant G, which, as we said, has a very small value, is the reason why objects don’t fly and collide with each other. It is also the reason why the earth is not attracted to us but we to it. After all, our mass is negligible compared to that of the earth.

Force F acting on m2 due to m1
Force F acting on m2 due to m1

The distance between the two objects has more impact than their masses because Newton’s gravitational equation follows an inverse square law. This means that if the distance doubles, the force is one-quarter of the strength of the original force.

What is the gravitational force of a single mass?

The force of a single mass is its gravitational field strength, which is defined as force per unit mass when it is placed in a gravitational field.

g is measured in units of newtons per kilogram ().F is the force experienced by mass m when it is placed in a gravitational field.

As the gravitational field on the earth’s surface is almost uniform, we can assume g to be constant. Hence, g is just the acceleration of mass m in a gravitational field.

Point masses

Point masses are objects that behave as if all mass is concentrated at their centre. Uniform shapes have a point mass.

The significance of point masses is that they have a radial gravitational field. In this, the field lines radiate from its centre. For point masses, our earlier equation becomes:

g = gravitational field strength (N/kg).

m = mass of the object (kg).G = gravitational constant ().r = distance from the centre (m).

The gravitational field strength of other planets

The gravitational force depends on the mass of the planet. For example, Mars has a gravitational field strength of 3.71 N/kg, which is lower than that of Earth due to its smaller diameter and lower mass. However, it's important to note that an object's weight also depends on the gravitational force g.

Weight is a measure of the force exerted on an object due to gravity, and it is directly proportional to the mass of the object and the gravitational force g. This means that if an object has a greater mass or if the gravitational force is stronger, the object will weigh more. Conversely, if the mass is lower or if the gravitational force is weaker, the object will weigh less.

So, for example, if you were on Mars, where the gravitational force is weaker than on Earth, you would weigh less than you do on Earth. This is because the gravitational force acting on your body is lower, so the force exerted on you by gravity is weaker, and therefore, your weight is also lower.

Mass and weight

The mass of an object remains constant wherever it is in the universe, but its weight varies depending on the strength of gravity in the location where it is present. For instance, if an object weighs 99.8 kg on Earth, it would weigh only 37.74 kg on Mars due to the weaker gravitational pull of Mars.

Similarly, the Moon's gravitational force is only 1.62 N/kg, which is much lower than that of Earth. As a result, it is easier to fly on the Moon than to walk. Walking on the Moon presents challenges because the pull is not strong enough to hold the human body down, and astronauts have to exert extra effort to maintain their balance and movement. On Mars, walking is still challenging, but it is relatively easier because the gravitational pull is stronger than on the Moon.

In summary, the strength of gravity determines an object's weight, and weight is directly proportional to the mass of an object and the gravitational force acting on it. Therefore, the weight of an object changes depending on the strength of gravity in that location.

Mass and distance

The tides on the surface of the Earth are a result of the gravitational pull of both the Moon and the Sun. Although the Sun has a much larger mass than the Earth, the distance between the two celestial bodies plays a significant role in the strength of the gravitational force. This is because the gravitational force is inversely proportional to the square of the distance between the objects.

As the Moon is much closer to the Earth than the Sun, it has a greater impact on the tides experienced on Earth's surface. The gravitational pull of the Moon causes the Earth's oceans to bulge and create high tides, and as the Moon moves around the Earth, the tides move with it. The Sun also has an impact on the tides, but its effect is much smaller than that of the Moon.

In summary, gravity is all about masses attracting one another, and only large masses such as the Sun, Moon, and other planets have a significant gravitational force. Newton's law of gravitation states that the gravitational force decreases as the distance between the objects increases. Gravit is the force per unit mass experienced by an object in a gravitational field, and in a radial field, the gravitational field can be represented as a vector pointing towards the center of mass.

Gravitational Fields

What is the gravitational field strength on earth? 

The gravitational field strength on earth is 10 N/kg. 

How do we calculate gravitational field strength? 

Gravitational field strength is calculated as follows:g=F/m

What is gravitational field strength measured in? 

It is measured in Newtons per kilogram (N/kg). 

What is a gravitational field? 

A gravitational field is a region where an object experiences a gravitational force due to the presence of another object. 

How can we calculate the weight of a body from its mass and gravitational field strength? 

This can be calculated using the equation below:weight = mass * gravitational field strengthw=m*g

Join Shiken For FREE

Gumbo Study Buddy

Explore More Subject Explanations

Try Shiken Premium for free

Start creating interactive learning content in minutes with Shiken. 96% of learners report 2x faster learning.
Try Shiken for free
Free 14 day trial
Cancel anytime
20k+ learners globally
Shiken UI showing questions and overall results.