What is the force of gravity at 220 miles above Earth's surface? Calculate how much of a g force the astronauts are actually experiencing. The solution for this math problem is a percentage.
You can calculate it using the Algebraic equation: gr = R2/r2 x g
R = the radius of the planet
r = the distance from the center of mass of the planet to the center of mass of the object in orbit
g = the gravitational attraction of the planet on objects on its surface
gr = the gravitational attraction of the planet as felt on the less massive object
The gravitational attraction of the Earth on the surface is 1g.
the Equatorial radius of the Earth in kilometers is 6378.1
you are given to use:
gr= Re^2/(Re+ alt)^2 * g
is there any reason you can't do that?
of course, convert 220 miles to km
To calculate the force of gravity at 220 miles above Earth's surface, we first convert the equatorial radius of the Earth from kilometers to miles.
Equatorial radius of the Earth in miles = 6378.1 kilometers * 0.621371 miles/kilometer
= 3963.167 miles
Next, we need to convert the distance of 220 miles above Earth's surface to the distance from the center of mass of the planet to the center of mass of the object in orbit.
r = R + distance above Earth's surface
= 3963.167 miles + 220 miles
= 4183.167 miles
Now we can calculate the gravitational attraction of the planet at this distance.
gr = (R^2 / r^2) * g
= (3963.167 miles^2 / 4183.167 miles^2) * 1g
= 0.8883g
The force of gravity at 220 miles above Earth's surface is equal to 0.8883 times the gravitational attraction on objects at the Earth's surface.
To calculate the g-force experienced by astronauts at this location, we need to find the percentage of 1g that 0.8883g represents.
Percentage of 1g = (0.8883g / 1g) * 100%
= 88.83%
Therefore, astronauts at 220 miles above Earth's surface are experiencing approximately 88.83% of the force of gravity compared to what they would feel on the Earth's surface.
To calculate the force of gravity at 220 miles above Earth's surface, we first need to convert the Equatorial radius of the Earth from kilometers to miles. Then we can use the given formula to find the force of gravity.
Equatorial radius of the Earth in kilometers: 6378.1 km
Using the conversion factor 1 km = 0.621371 miles, we can convert the radius to miles:
Equatorial radius of the Earth in miles: 6378.1 km * 0.621371 miles/km ≈ 3963.19 miles
Now, let's plug the values into the formula:
R = 3963.19 miles (radius of the planet)
r = 220 miles (distance from the center of mass of the planet to the center of mass of the object in orbit)
g = 1g (gravitational attraction of the planet on objects on its surface)
Calculating gr, the gravitational attraction of the planet as felt on the less massive object:
gr = (R^2 / r^2) * g
gr = (3963.19^2 / 220^2) * 1
Simplifying the equation:
gr ≈ 21.352
Therefore, the gravitational attraction felt by the object in orbit 220 miles above Earth's surface is approximately 21.352 times the gravitational attraction on the planet's surface.
To calculate the corresponding g-force experienced by the astronauts, we need to convert gr into a percentage. This can be done using the equation:
Percentage = (gr - 1) * 100
Calculating the percentage:
Percentage = (21.352 - 1) * 100
Percentage ≈ 2035.2%
Thus, the astronauts in orbit 220 miles above Earth's surface are experiencing approximately 2035.2% of the gravitational force felt on the Earth's surface.