Apparent Weight?

Question

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 x 10^7m. What is the period of the motion? What is the value of g at this orbit? What is the apparent weight of a 2000kg satellite at this g?




Now, I found the period to be 24hr, and the value of g to be 0.223m/s/s. But I cannot seem to find a formula to correctly calculate the apparent weight of the satellite with this information.

Answer 1

I assume that by apparent weight you mean the weight W that would be measured if the satellite were stationary.
Given the information you have developed, there are at least 3 ways to compute W.
Hardest (since you have to recall G and earth mass Me):
r = altitude + earth radius (you must have calc'ed this already)
W = Gm*Me/r^2
Easier:
Since centripetal force=W,
W = mω^2r
ω is easily calculated from the period.
Easiest:
W = ma
You have a = 0.223 m/s^2

Answer 2

By the defenition of geo synchronous orbit, it must have the same period of earth's rotation. hence the period is 24 hour.
However, You can calculate it too.
g is calcualated by G M /R^2 .
Apparent weight = mg - mv^2 /R.

Note g = GM/R^2 and mg = GMm/R^2 which was equated to mv^/R.

Since mg equals mv^2/R, the apparent weight is zero.
If a person is in the satelite and stands on a scale, he will not press the scale and the reading shows zero.

Answer 3

no longer sufficient information. there is not any given information on WHICH way that's shifting and slowing down. "i comprehend that acceleration is downward as a effect" What!? the place did you get that information? "so obvious weight is lesser applicable?" sure certainly. keep in mind, you may no longer sense your weight. you in trouble-free terms sense the help tension that constrains against what you think of is your weight. The help tension in the elevator from the floor acts upward. in case you're accelerating downward, then real gravity would desire to dominate the help tension. consequently, the help tension is comfortable from what that's whilst the equipment is at relax, and he feels lighter than his truthfully weight.