Using calculus to find gravity in space (dynamics)

In summary, the conversation discusses solving the problem of finding the gravity in the ISS using the formula g=GM/R^2. One approach is to calculate GM by multiplying g and R^2 and then using it in GM/(R+400)^2 to get 8.7m/s^2. The person also wonders if calculus can be used, but is unsure how to apply it in physics. Another person suggests simply looking up the mass of Earth to solve for g, questioning the need for using calculus.
  • #1
Veirian
1
0
I am currently solving a problem where I need to find the gravity in the ISS (distance 400km from Earth with Radius 6371km). I am using the formula g=GM/R^2 . One way to solve it would be to find GM by multiplying g(which is 9.81) and R^2 (which is known) and then to use it in GM/(R+400)^2 and get 8.7m/s^2.

I was wondering whether there was a way to use calculus to get this. If I integrate with respect to the distance (From 6371 to 6371+400) I get something around -1.02. Does that mean that the value changes from R to R+400 by -1.02 ?
I am having some trouble in deciding when and how to use calculus in physics (more specifically dynamics).
 
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  • #2
I don't understand what the difficulty here is, and why you need to use calculus.

Why can't you just plug in the numbers and find g? Is it because you don't know "M", the mass of Earth? This is something you can easily look up. I don't understand why you're making it more difficult than it is.

Zz.
 

What is calculus?

Calculus is a branch of mathematics that deals with the study of continuous change. It is used to analyze and model various physical and mathematical phenomena, such as motion, growth, and optimization.

How is calculus used to find gravity in space?

Calculus is used to find gravity in space by using the fundamental theorem of calculus, which relates the concepts of integration and differentiation. By applying this theorem to the equations of motion in space, we can determine the strength and direction of gravitational forces between objects.

What are the key equations used in calculating gravity in space using calculus?

The key equations used in calculating gravity in space using calculus are Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them, and the equations of motion, which describe the position, velocity, and acceleration of objects in space.

What are the main challenges in using calculus to find gravity in space?

One of the main challenges in using calculus to find gravity in space is dealing with the complexities of multi-body systems, where the gravitational forces between multiple objects interact with each other. This requires advanced mathematical techniques, such as vector calculus and differential equations, to accurately model and predict the motion of objects in space.

How is the concept of gravity in space different from gravity on Earth?

The concept of gravity in space is different from gravity on Earth in that it is not influenced by external factors such as air resistance and surface friction. In space, the only factors that affect an object's motion are its mass and the gravitational forces acting upon it. This makes the application of calculus to find gravity in space more straightforward compared to calculating gravity on Earth.

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