The force of gravity is inversely proportional to the square of the center of the earth. if you weigh 120 lbs on the surface of the earth, how much would you weigh 250 miles above the surface? (Earth's radius = 4000 miles)
The force of gravity is inversely proportional to the square of the center of the earth. if you weigh 120 lbs on the surface of the earth, how much would you weigh 250 miles above the surface? (Earth's radius = 4000 miles)
20psi
To calculate the weight 250 miles above the surface of the Earth, we need to understand how gravity decreases with distance.
The force of gravity can be described by the inverse square law, which states that the force of gravity is inversely proportional to the square of the distance from the center of the Earth.
In this case, we can use the ratio of the radius of the Earth to the distance 250 miles above the surface to calculate the weight.
Let's proceed with the calculations:
1. Determine the distance from the center of the Earth:
The radius of the Earth is given as 4000 miles. Thus, the distance from the center of the Earth to the surface is 4000 miles.
To find the distance from the center of the Earth to the location 250 miles above the surface, we need to add this distance to the radius of the Earth:
Total distance = 4000 miles + 250 miles = 4250 miles
2. Apply the inverse square law:
Using the inverse square law, we can calculate the weight at the new distance using the formula:
Weight 1 / Weight 2 = (Distance 2 / Distance 1)²
Where:
Weight 1 = Weight on the surface of the Earth (given as 120 lbs)
Weight 2 = Weight 250 miles above the surface (to be determined)
Distance 1 = Distance from the center of the Earth to the surface (4000 miles)
Distance 2 = Distance from the center of the Earth to 250 miles above the surface (4250 miles)
Now, let's plug in the values into the formula:
120 lbs / Weight 2 = (4250 miles / 4000 miles)²
3. Solve for the weight 250 miles above the surface:
To solve for Weight 2, we can rearrange the formula as follows:
Weight 2 = 120 lbs / [(4250 miles / 4000 miles)²]
Simplifying the formula, we have:
Weight 2 = 120 lbs / (1.0625)²
Weight 2 = 120 lbs / 1.1289
Weight 2 ≈ 106.15 lbs (rounded to two decimal places)
Therefore, at a distance of 250 miles above the surface of the Earth, your weight would be approximately 106.15 lbs.