Gravitation on three uniform spheres

In summary, the three spheres with uniform density and equal mass have different rotational periods. The sphere with the longest period of 48 hours would have the greatest acceleration at the poles and equator. This is because the acceleration is proportional to the radius, and the larger the radius, the greater the acceleration. The fact that the spheres have uniform density does not affect this answer.
  • #1
stunner5000pt
1,461
2
Lets say we have three spheres all of uniform density and equal mass, However, sphere A has a rotational period of 16h, B has period of 24h and C has period of 48h.
So which one has the greatest acceleration (g value) at the poles and at the equator.
 
Physics news on Phys.org
  • #2
I am sorely tempted to say that, since they all have the same size and density, they all have the same GRAVITATIONAL acceleration.

What you are asking about, however, is net acceleration.

A mass on a sphere of radius R, rotating with angular velocity ω, requires an inward (centripetal) acceleration of Rω2 just to stay on the surface. If you were to drop a mass at the surface of each of those spheres, the acceleration you would observe would be the "gravitational" acceleration (the same for all these spheres) minus the centripetal acceleration. Since that is proportional to R, you would observe the greatest acceleration on the sphere with least rotational speed: largest period- 48 hours.

I just noticed that you said "uniform density", not same density or same size. However, since uniform or non-uniform density is not really relevant to the problem, I going to assume you meant that the three spheres were all the same size and stick with my answer.
 
Last edited by a moderator:

1. What is gravitation on three uniform spheres?

Gravitation on three uniform spheres refers to the force of attraction between three spherical objects that have equal mass and are evenly distributed. This force is known as gravitational force and is governed by the law of universal gravitation.

2. How is the gravitational force calculated between three uniform spheres?

The gravitational force between three uniform spheres is calculated using the law of universal gravitation, which states that the force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.

3. What factors affect the strength of the gravitational force between three uniform spheres?

The strength of the gravitational force between three uniform spheres is affected by the masses of the objects and the distance between them. The force increases as the masses increase and decreases as the distance between them increases.

4. How does the arrangement of the spheres affect the gravitational force?

The arrangement of the spheres does not affect the gravitational force between them as long as they have equal mass and are evenly distributed. However, if one sphere is closer to the other two, it will experience a stronger gravitational force from those two spheres compared to the force it exerts on them.

5. What are some real-world applications of understanding gravitation on three uniform spheres?

Understanding gravitation on three uniform spheres is crucial in many fields such as astrophysics, engineering, and space exploration. It helps in predicting the motion of planets, satellites, and other celestial objects. It is also important in designing structures and vehicles that can withstand the gravitational forces of different objects in space.

Similar threads

I Understanding Ewald's sphere in the context of X-Ray diffraction
    • Other Physics Topics
Replies
3
Views
3K
I Static sphere with gravitating fluid
    • Classical Physics
Replies
6
Views
291
B Why exactly do we need the gravitational constant?
    • Other Physics Topics
Replies
11
Views
2K
Does the gravitational rate of acceleration increase within a planet?
    • Classical Physics
2
Replies
54
Views
2K
Period and Velocity of Oscillating Sphere Attached to Spring
    • Introductory Physics Homework Help
Replies
10
Views
1K
Gravitational Effect of Uniform Mass on Earth's Surface
    • Other Physics Topics
Replies
4
Views
1K
Inverse square law of gravitation and force between two spheres
    • Introductory Physics Homework Help
Replies
8
Views
933
Writing: Input Wanted Revisiting the Enzmann Starship Design: A Sixty-Year Perspective
    • Sci-Fi Writing and World Building
Replies
24
Views
608
Pure rolling of sphere having non uniform mass density ?
    • Mechanics
Replies
2
Views
2K
I I'm calculating more energy out than I put in
    • Classical Physics
2
Replies
61
Views
1K

Hot Threads

Recent Insights

Back
Top