What is the gravitational force of attraction between two bodies of masses 40 kg and 80 kg separated by a distance of 15 m?

This gravitational force calculator lets you find the force between any two objects. Read on to get a better understanding of the gravitational force definition and to learn how to apply the gravity formula. Make sure to check out the escape velocity calculator, too!

Newton's law of universal gravitation states that everybody of nonzero mass attracts every other object in the universe. This attractive force is called gravity. It exists between all objects, even though it may seem ridiculous. For example, while you read these words, a tiny force arises between you and the computer screen. This force is too small to cause any visible effect, but if you apply the principle of gravitational force to planets or stars, its effects will begin to show.

One of the most common examples illustrating the principle of the gravitational force is the free fall.

Use the following formula to calculate the gravitational force between any two objects:

F = GMm/R²

where:

F stands for gravitational force. It is measured in newtons and is always positive. It means that two objects of a certain mass always attract (and never repel) each other;
M and m are the masses of two objects in question;
R is the distance between the centers of these two objects; and
G is the gravitational constant. It is equal to 6.674×10-11 N·m²/kg².

Did you notice that this equation is similar to the formula in Coulomb's law? While Newton's law of gravity deals with masses, Coulomb's law describes the attractive or repulsive force between electric charges.

Find out the mass of the first object. Let's choose Earth - its mass is equal to 5.972×1024 kg. You can enter this large number into the calculator by typing 5.972e24.
Find out the mass of the second object. Let's choose the Sun - it weighs 1.989×1030 kg, approximately the same as 330,000 Earths.
Determine the distance between two objects. We will choose the distance from Earth to Sun - about 149,600,000 km.
Enter all of these values into the gravitational force calculator. It will use the gravity equation to find the force.
You can now read the result. For example, the force between Earth and Sun is as high as 3.54×1022 N.

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Force of attraction is defined as a force that causes two or more objects to come together, even if they are not near to or touching one other. It is a force that attracts the bodies closer together. According to Newton’s universal law of gravity, every mass that exists in the cosmos attracts another mass, and everything which is thrown upwards is bound to fall back on the ground. Magnetic force, electric force, electrostatic force, and gravitational force are some attraction forces.

Force Of Attraction Formula

The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the distance between them. It is denoted by the symbol Fg. Its unit of measurement is Newton (N), and the dimensional formula is given by [M1L1T-2]. Its formula is equal to the product of the gravitational constant and the ratio of the product of masses of the bodies to the square of the distance between them.

Fg = Gm1m2/r2
Where,
Fg is the force of attraction,
G is the gravitational constant with the value of 6.67 ×10−11 Nm2/kg2,
m1 is the mass of a body,
m2 is the mass of other body,
r is the distance between the two bodies.

Derivation

Consider a system of two bodies of masses m1 and m2 such that they are separated by a distance r. It is known that the force of attraction between these two bodies is directly proportional to the product of the masses of the bodies.
F ∝ m1m2 ⇢ (1)
Also, the force is indirectly proportional to the square of the distance between the two bodies. So we get,
F ∝ 1/r2 ⇢ (2)
From (1) and (2),
F ∝ m1m2/r2
Replacing the proportionality sign with a constant, we get,
Fg = Gm1m2/r2
Here, G is known as the gravitational constant.
This derives the formula for force of attraction between two bodies.

Sample Problems

Problem 1: Calculate the gravitational force between two bodies of masses 50 kg and 100 kg separated by a distance of 20 m.

Solution:

m1 = 50
m2 = 100
r = 20
Using the formula we get,
F = Gm1m2/r2
= (6.67 ×10−11 × 50 × 100)/(20)2
= 8.343 × 10-10 N

Problem 2: Calculate the gravitational force between two bodies of masses 100 kg and 150 kg separated by a distance of 80 m.

Solution:

m1 = 100
m2 = 150
r = 80
Using the formula we get,
F = Gm1m2/r2
= (6.67 ×10−11 × 100 × 150)/(80)2
= 1.5643 × 10-10 N

Problem 3: Calculate the gravitational force between two bodies of masses 200 kg and 170 kg separated by a distance of 1000 m.

Solution:

m1 = 200
m2 = 170
r = 1000
Using the formula we get,
F = Gm1m2/r2
= (6.67 ×10−11 × 200 × 170)/(1000)2
= 2.26 × 10-12 N

Problem 4: Calculate the mass of the bodies if the gravitational force between them is 2.8 × 10-12 N such that they have equal masses and are separated by a distance of 120 m.

Solution:

F = 2.8 × 10-12
r = 120
Using the formula we get,
F = Gm2/r2
=> m2 = Fr2/G
=> m2 = (2.8 × 10-12 × 120 × 120)/(6.67 ×10−11)
=> m2 = 625
=> m = 25 kg

Problem 5: Calculate the mass of the bodies if the gravitational force between them is 1.89 × 10-11 N such that they have equal masses and are separated by a distance of 60 m.

Solution:

F = 1.89 × 10-11

r = 60
Using the formula we get,
F = Gm2/r2
=> m2 = Fr2/G
=> m2 = (1.89 × 10-11 × 60 × 60)/(6.67 ×10−11)
=> m2 = 1024
=> m = 32 kg

Problem 6: Calculate the distance between the bodies of masses 16 kg and 32 kg if the gravitational force between them is 4.2 × 10-12 N.

Solution:

F = 4.2 × 10-12
m1 = 16
m2 = 32
Using the formula we get,
F = Gm1m2/r2
=> r2 = Gm1m2/F
=> r2 = (6.67 ×10−11 × 16 × 32)/(4.2 × 10-12)
=> r2 = 8100
=> r = 90 m

Problem 7: Calculate the distance between the bodies of masses 40 kg and 34 kg if the gravitational force between them is 2.6 × 10-11 N.

Solution:

We have,
F = 2.6 × 10-11
m1 = 40
m2 = 34
Using the formula we get,
F = Gm1m2/r2
=> r2 = Gm1m2/F
=> r2 = (6.67 ×10−11 × 40 × 34)/(2.6 × 10-11)
=> r2 = 3600

=> r = 60 m