We are all aware of the terms acceleration and gravity, but in this post, we will learn more detailed facts regarding centripetal acceleration and gravity.
When a body is allowed to move in a circular trajectory, the direction keeps changing so that there will be a change in the velocity resulting in the acceleration of the body. This body acceleration in circular motion is mainly concentrated at the circle’s center. This type of acceleration influences gravity.
In the planet’s motion around the sun, we can observe how centripetal acceleration and gravity are related. The centripetal acceleration is due to the exertion of centripetal force on the planet. The exertion of centripetal force is due to gravity influencing the body.
Is centripetal acceleration equal to gravity?
Gravity can be referred to as centripetal force exerted on the body traveling in a circular path. For example, consider the motion of a satellite around a celestial body. They trace a circular path around the celestial body. The circular motion is due to the centripetal force, and thus, the satellite acquires centripetal acceleration.
Since a gravitational attraction is exerted on the satellite to be in a circular motion around the celestial body, the gravitational attraction is the same as the centripetal force exerted on the satellite. Thus, it shows that centripetal acceleration and gravity are equal.
In another aspect, we can state that acceleration due to gravity and centripetal acceleration is the same in a geostationary orbit. This is because the acceleration of the satellite revolving around the earth exactly matches the rotational speed of the earth.
When gravity is equal to centripetal acceleration?
If any object is moving in a circular path, there must be some change in the object’s angle. It is said that if the force of exertion is much larger than the change in acceleration, then the acceleration would be entirely concentrated over the center and become equal to the gravity.
When the centripetal force is exerted on the object, the pathway of the object does not remain as a uniform circular path but is oval shape. Since we know that the trajectory of the planetary motion is also somewhat oval, say elliptical. It shows that centripetal acceleration and gravity are equal when there is a change in angle, and the trajectory is oval.
Similarities between gravity and centripetal acceleration
Since gravity is considered a centripetal force and centripetal acceleration results from the centripetal force, both centripetal acceleration and gravity are equal when the body is under uniform circular motion.
- The centripetal acceleration is always directed towards the center of curvature same as the gravity directed towards the center.
- Both centripetal acceleration and gravity are associated with the radius of curvature.
- In some cases, the gravity is also a non-linear similar to the centripetal acceleration.
- Both centripetal acceleration and gravity are inertial forces. According to the general theory of relativity, any free-falling object experiences an inertial force, so the force of gravity is inertial. Centripetal acceleration is due to centripetal force that causes the object to retain in a circular path, an inertial effect carrying the object away from the center of the rotational axis.
- As gravity attracts the body towards the gravitational field, the centripetal acceleration always pulls the body towards its center of the circular orbit.
Difference between gravity and centripetal acceleration
Even though gravity serves as a centripetal force, there is some difference between centripetal acceleration and gravity. A few differences between centripetal acceleration and gravity are listed below.
|Gravity comes from all the masses combined due to gravitational pull.||Centripetal acceleration is due to the circular motion of an object directed toward the geometrical center.|
|Gravity is a constant physical entity in a linear dimension that is hard to measure with high accuracy.||Centripetal acceleration is a variable because the direction frequently changes along the circular path.|
|Gravity can produce both linear and non-linear motion of the masses.||Centripetal acceleration can only produce non-linear motion in a circular path.|
|The force of gravity always prevents from free falling of the object. Due to this reason, suppose any object falling free does not experience any internal stress.||Centripetal acceleration deflects the object from the world line to the force-free path so that the object experiences internal stress.|
|The gravity is strictly proportional to the mass.||The masses are not restricted to strict proportionality with the centripetal acceleration.|
|Gravity follows the inertial and force-free path through space-time.||Centripetal acceleration prevents the object from following an inertial and force-free path through space-time.|
Find gravity using centripetal acceleration.
The centripetal acceleration is due to a change in velocity of a body under uniform circular motion in which the entire body mass is concentrated towards its center. Hence to find centripetal acceleration, we need to know the body’s velocity.
Let us assume that v is the velocity of the body in a circular path whose radius is r; then, centripetal acceleration is given by
Since centripetal acceleration is due to centripetal force exerted on the body, using Newton’s second law F=ma, we can give centripetal force as,
We know that gravity can also act as a centripetal force so we can rewrite the gravity formula as
Where G is the gravitational force constant, m1 and m2 are the masses, and r is the radius.
Equating the above two equation we get
But v2/r=ac ; then the equation for gravity is given by
This equation holds good only for small objects.
How does centripetal acceleration balance gravity?
Gravity is the fundamental force of nature exerted on every object on the earth. Meanwhile, if we talk about centripetal acceleration, which is due to centripetal force, a form of generic force acting on the rotator system. Since the earth is a rotator system, there must be a balance between centripetal acceleration and gravity.
In astronomy, all-stars and planets require some force to trace the circular path that must be proportional to the centripetal acceleration. This force is managed by gravity by balancing gravitational attraction and centripetal force between the planet and celestial stars. This balance is obtained by estimating the mass and the radius of given stars and planets.
In the same way, the centripetal force is balanced by a reaction force called centrifugal force. You may have experienced them if you ever ride on the merry-go-round.
Merry-go-round is not a centripetal force example but a good example of centripetal acceleration. While riding on the merry-go-round, one can experience a pseudo force pushing the person away from the center. This center-fleeing force balances the centripetal acceleration and gravity in opposite directions.
Why is centripetal acceleration always pointed towards the center?
Centripetal acceleration causes the constant speed of the body under circular motion. If acceleration is not oriented towards the center, it wouldn’t be centripetal.
In a circular trajectory, the direction is variable, which causes acceleration. Newton stated in his laws that the acceleration of any object must be in the direction of the net force. In a circular path, the net force acting on the object is towards the center. Thus, centripetal acceleration is also directed towards the center.
Why is centripetal acceleration not constant?
In a circular path, radial acceleration can be kept constant but not centripetal.
In most cases, the magnitude is constant, but its direction is not constant throughout the process. Since there is frequent change in the direction of motion along the circular path, the velocity keeps changing, which accelerates the body. This acceleration varies with the velocity along with the direction change.
Let us wrap up this post by stating that centripetal acceleration is gravity are related to one another as the main cause of centripetal acceleration is centripetal force. In some contexts, gravity can be referred to as centripetal force.