What is the orbital distance for a satellite with a 125 min period around Earth?

  • Thread starter choyphin
  • Start date
  • Tags
    Period
In summary, the distance from Earth at which a satellite would have a period of 125 minutes can be calculated using the formula R = cube root ( GM * (T/2pi)^2 ), where G is the gravitational constant, M is the mass of the Earth, and T is the period in seconds. By substituting the given values, the resulting answer is 106.6 km, which is the radius of the orbit from the center of the Earth. To find the altitude, the radius of the Earth (6.38*10^6 m) must be subtracted from this value.
  • #1
choyphin
11
0

Homework Statement


At what distance about Earth would a satellite have a period of 125 min?
G=6.673x10^-11
T=125 Min
Mass=5.97x10^24
Radius of Earth=6.38*10^6

Homework Equations


T=2pi*Square root of (R^3/constant*mass)


The Attempt at a Solution


125=2*3.14*Square root of ((6.38x10^6)^3+R^3/6.673x10^-11*5.97x10^24)
I got a negative #... Which i know is wrong!
 
Physics news on Phys.org
  • #2
Put the units in - it will help !
 
  • #3
I did that, but still got an unreasonable answer: 2.6x10^26
 
  • #4
T=2pi*sqrt(R^3/GM)
so T/2pi = sqrt(R^3/GM)
Square both sides (T/2pi)^2 = R^3/GM
Finally R = cube root ( GM * (T/2pi)^2 )

Check the units (m^3 kg^01 s^-2 * kg * s^2)^1/3 = (m^3 )^1/3 = m
 
  • #5
Is the answer 106.6 KM? Thanks so much for the explanations by the way!
 
  • #6
I think you have a slight mistype there, do you have T in seconds?
Remember that the result is the radius of the orbit from the centre of the Earth - if you want the altitude you need to subtract the radius of the Earth.
 

1. What is the period of an orbiting object?

The period of an orbiting object is the time it takes for the object to complete one full orbit around another body. This is typically measured in days, months, or years depending on the size and speed of the orbiting object.

2. How is the period of an orbiting object calculated?

The period of an orbiting object can be calculated using Kepler's third law of planetary motion. This law states that the square of the orbital period is proportional to the cube of the average distance between the two bodies. This can be expressed as T^2 = (4π^2/G) x a^3, where T is the period, G is the gravitational constant, and a is the average distance between the two bodies.

3. What factors affect the period of an orbiting object?

The period of an orbiting object is primarily affected by the mass and distance of the two bodies involved. The larger the mass of the central body, the shorter the period will be. Additionally, the farther the distance between the two bodies, the longer the period will be.

4. Can the period of an orbiting object change?

Yes, the period of an orbiting object can change due to various factors such as gravitational perturbations from other objects, changes in the mass or distance of the bodies, and external forces like solar wind. However, the change in period is usually very small and can take a long time to occur.

5. How does the period of an orbiting object affect its velocity?

According to Kepler's second law of planetary motion, an object's velocity will vary as it moves along its elliptical orbit. The object will move faster when it is closer to the central body and slower when it is farther away. This means that the period of an orbiting object indirectly affects its velocity, as the two are inversely proportional.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
966
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Replies
1
Views
956
Back
Top