Increasing Gravity and Acceleration

In summary, the conversation discusses a problem involving two solid, spherical masses in a vacuum, with Sphere A having a mass of 10 kg and Sphere B having negligible mass. The distance between the centers of the two spheres is 10 meters and the gravity constant in this universe is 1 N*m2/kg2. The question is how to determine the distance, x, between the centers of the two spheres at time t. The speaker has attempted to solve the problem using various methods and equations, including the gravitational acceleration equation, derivatives of acceleration, and approximation on intervals of 1 second. However, they have been unable to find a solution and are seeking help in solving the problem.
  • #1
kaikalii
17
0
So, assume a system of two solid, spherical masses in a vacuum. Sphere A has a mass of 10 kg, and Sphere B has negligible mass in comparison. The centers of the two spheres are 10 meters apart. For the sake of simplicity, let's say that in this universe, the gravity constant, G, is 1 N*m2/kg2. How would you determine the distance, x, between the centers of the two spheres at time t?

I have been trying to solve this problem using many methods, but have been unsuccessful.

I have been using the gravitational acceleration equation: g = G*m/r2
as well as the derivatives of acceleration: a = g, v = gt + v0, x = 1/2*gt2 + v0t + x0

I tried approximating on intervals of 1 second, i.e. x(0) = 10, x(1) = 9.95, x(2)= 9.8, x(3) = 9.547, etc.
However, I was unable to reconcile this pattern to an integral using an infinitely short time.

How do I solve this problem?

(It's not for homework, just curiosity.)
 
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  • #2
It is still similar to homework questions, I think you'll get better answers there.

Do you know the concept of differential equations?
If yes, you can find one and solve it.
Without them, it is ... problematic.
 

1. How does increasing gravity affect objects?

Increasing gravity will cause objects to fall faster and accelerate at a higher rate. This means that they will gain speed more quickly and hit the ground with greater force.

2. Is it possible to increase the gravity on Earth?

No, gravity is a fundamental force of nature and cannot be artificially increased on Earth. The only way to experience higher gravity is to go to a planet with a stronger gravitational pull, such as Jupiter.

3. How would increasing gravity impact human beings?

Increasing gravity would make it more difficult for humans to move and perform tasks. It could also lead to health problems such as bone and muscle deterioration due to the increased strain on the body.

4. Can increasing gravity lead to time dilation?

Yes, according to Einstein's theory of relativity, time is affected by gravity. The higher the gravity, the slower time moves. This means that increasing gravity could potentially lead to time dilation, where time passes slower for objects closer to a strong gravitational field.

5. What are the potential benefits of increasing gravity in space exploration?

Increasing gravity in space could potentially help astronauts maintain bone and muscle strength, as well as prevent the negative effects of microgravity on the human body. It could also make it easier to build and maintain structures in space, as they would experience a stronger gravitational pull.

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