What is the Height of the International Space Station Above the Earth's Surface?

In summary, the conversation discusses finding the height of the International Space Station above the Earth's surface, given its circular orbit and number of revolutions per day. The solution attempts to use gravity as the centripetal force and calculates the height using the incorrect value of 9.8 m/s for acceleration due to gravity. The correct formula for gravity is given as g = G*M_Earth/r^2, and it is suggested to use Kepler's 3rd law to solve for the height.
  • #1
Chan M

Homework Statement


The International Space Station, launched in 1998, makes 15.65 revolutions around the Earth each day in a circular orbit. Find the height of the space station (in kilometers) above the earth’s surface.

Homework Equations


T = (2*pi*r) / v
r - radius, distance between center of Earth and the station
r = Re + h
Re - radius of earth
h = height above ground
Find h

The Attempt at a Solution


So there is only one force acting on the station, which is gravity. Acceleration due to gravity is also centripetal acceleration. Gravity is the centripetal force.

15.65 revolution each day is one revolution every 5520.77 seconds

Fg = m*Ac
mg = m * (v^2 / r)
g = v^2 / r
g = [ (2*pi*r) / T ]^2 / r
g = 4*pi*pi*r / T^2
h = [(T^2)*g / 4*pi*pi ] - Re
h = [(5520.77^2)*9.8 / 4*pi*pi ] - (6.37 * 10^6)
h =
upload_2017-10-2_21-38-59.png
(this is what I put in the calculator)
h = 1195987.99 meters
h = 1196 km

This is not the correct answer, I know the correct answer, I just don't know how to get it or what I'm doing wrong. Thanks!
 

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  • #2
Gravity is weaker that high up so ##g=9.8##m/s won't work. You need
$$g=G\frac{M_{Earth}}{r^{2}}$$
 
  • #3
can one use Kepler's 3rd law?
 

Related to What is the Height of the International Space Station Above the Earth's Surface?

What is the "Height above Earth Problem"?

The "Height above Earth Problem" is a mathematical problem that involves determining the height of an object above the surface of the Earth based on its position and velocity.

Why is the "Height above Earth Problem" important?

The "Height above Earth Problem" is important in the fields of physics, astronomy, and engineering as it allows us to calculate and predict the trajectory of objects in space, such as satellites and spacecraft.

How is the "Height above Earth Problem" solved?

The "Height above Earth Problem" is solved using equations and principles from kinematics and calculus. This involves calculating the object's position and velocity at different points in time and using them to determine its height above the Earth.

What factors affect the accuracy of solving the "Height above Earth Problem"?

The accuracy of solving the "Height above Earth Problem" can be affected by factors such as atmospheric conditions, gravitational pull from other bodies, and the precision of the initial position and velocity data.

What are some real-world applications of the "Height above Earth Problem"?

The "Height above Earth Problem" has many practical applications, including predicting the trajectory of spacecraft and satellites, calculating the height of objects in orbit, and determining the optimal launch angle for rockets.

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