# How Do You Solve These Challenging Gravitation Problems?

• Glenn K
In summary, to find the distance from the center of the Earth where your weight would decrease from 900N to 300N, you can use the universal law of gravitation to solve for your mass and then use that to find the distance from the center of the Earth. For the second question, you can use the simplified version of the force equation for two electrons to find the mass of one electron.
Glenn K
Okay, I've looked over all of my formulas numerous times and I just can't figure out what to do for these two:

In terms of Earth radii, how far from the center of the Earth would you have to travel in order to cut your weight from 900N to 300N?

The gravitational force between two electrons 1m apart is 5.42x10^-71N. Find the mass of an electron.

Could anyone help me out here? I'm trying to figure out what to do, but I'm just drawing blanks.

I'm assuming that it claims you have a force of 900N at a normal ground level, which would make the Earth's radius 6.47 * 10^6m. You're going to use the universal law of gravitation and solve for m1 (your mass).

$$900 = \frac{(6.67*10^{-11})(5.98*10^{24})m_1}{6.47*10^6}$$

Force is in Newtons, and everything else is in standard SI units.

Solve for m1. The plug that number into the gravitation equation again with 300N as your force and solve for d.

Jameson

Last edited by a moderator:
In terms of Earth radii, how far from the center of the Earth would you have to travel in order to cut your weight from 900N to 300N?

If your weight is 900N at the surface, find your mass. It's a pretty simple conversion. Then solve the gravitational force equation for the radius and use F = 300N to find your new r.

The mass of two electrons is equal, so the force equation simplifies to

$$F = G\frac{m^2}{r^2}$$

You are given F, G, and R.

## 1. How do you solve Two Gravitation Problems?

To solve Two Gravitation Problems, you need to use Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## 2. What are the two types of Two Gravitation Problems?

The two types of Two Gravitation Problems are the two-body problem and the three-body problem. The two-body problem involves two objects orbiting around each other, while the three-body problem involves three objects orbiting around a common center of mass.

## 3. What is the difference between Two Gravitation Problems and Two-Body Mechanics?

Two Gravitation Problems involve the study of the motion of objects under the influence of gravity, while Two-Body Mechanics involves the study of the motion of two objects interacting with each other through a force other than gravity.

## 4. What are some real-life applications of Two Gravitation Problems?

Two Gravitation Problems are used to model the motion of planets and satellites in our solar system and to predict the path of comets and asteroids. They are also used in spacecraft trajectory planning and the study of celestial mechanics.

## 5. What are the limitations of Two Gravitation Problems?

Two Gravitation Problems assume that the objects being studied are point masses with no physical size. They also do not take into account other forces that may affect the motion of the objects, such as air resistance. Additionally, the three-body problem is notoriously difficult to solve analytically and often requires numerical methods.

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