# Relationship between planetary mass and gravity formula example

### Newton's Law of Universal Gravitation

For example, Earth's gravity, as already noted, is equivalent to m/s2 (or ft/s2). Based on their sizes and masses, the gravity on another planet is often . Calculations based on its mean radius ( km), mass ( x . of the gravity could mean the difference between life and death. Astronomy Planets to Cosmos The Force of Gravity is an example of an Inverse Square Law Force where aapple= meters/sec2, and the ratio of the Mass of the apple to the Combining these together using Newton's formula for the Gravitational Force allows us to estimate the mass of the Earth, as follows. The r in the formula above stands for the distance between two point masses, The gravitational force exerted by any planet is based on the effective mass of the . (For example think of an object like a metal bar's gravity on another object at.

Basically, gravity is dependent on mass, where all things — from stars, planetsand galaxies to light and sub-atomic particles — are attracted to one another. Depending on the size, mass and density of the object, the gravitational force it exerts varies. And when it comes to the planets of our solar systemwhich vary in size and mass, the strength of gravity on their surfaces varies considerably. For example, Earth's gravity, as already noted, is equivalent to 9.

This means that an object, if held above the ground and let go, will accelerate towards the surface at a speed of about 9.

This is the standard for measuring gravity on other planets, which is also expressed as a single g. Based on their sizes and masses, the gravity on another planet is often expressed in terms of g units as well as in terms of the rate of free-fall acceleration.

So how exactly do the planets of our solar system stack up in terms of their gravity compared to Earth? With a mean radius of about 2, km and a mass of 3. This makes Mercury the smallest and least massive planet in the solar system. However, thanks to its high density — a robust 5. Venus is similar to Earth in many ways, which is why it is often referred to as "Earth's twin".

With a mean radius of 4. Hence, it is no surprise why the gravity on Venus is very close to that of Earth's — 8. Gravity on the Moon: This is one astronomical body where human beings have been able to test out the affects of diminished gravity in person.

Calculations based on its mean radius kmmass 7. Mars is also similar to Earth in many key respects. However, when it comes to size, mass and density, Mars is comparatively small.

In fact, its mean radius of 3. Its density, meanwhile, is about 0.

### Acceleration Due to Gravity Formula

Because of this, Mars has 0. Jupiter is the largest and most massive planet in the solar system. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled increased by a factor of 2then the force of gravitational attraction is decreased by a factor of 4 2 raised to the second power.

If the separation distance between any two objects is tripled increased by a factor of 3then the force of gravitational attraction is decreased by a factor of 9 3 raised to the second power. Thinking Proportionally About Newton's Equation The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration.

Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.

Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality. This equation is shown below.

• Newton's Law of Universal Gravitation
• How Strong is Gravity on Other Planets?
• Acceleration Due to Gravity Formula

The constant of proportionality G in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death.

This experiment will be discussed later in Lesson 3. Using Newton's Gravitation Equation to Solve Problems Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem. The solution of the problem involves substituting known values of G 6.

## How strong is gravity on other planets?

The solution is as follows: This would place the student a distance of 6. Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student a. This illustrates the inverse relationship between separation distance and the force of gravity or in this case, the weight of the student. The student weighs less at the higher altitude. However, a mere change of 40 feet further from the center of the Earth is virtually negligible.

A distance of 40 feet from the earth's surface to a high altitude airplane is not very far when compared to a distance of 6. This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth.

As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.