What is the apparent weight of an astronaut in a satellite revolving around the earth ?
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Dear Student,
Please find below the solution to the asked query:
When the satellite revolves in an orbit around the earth in a fixed orbit. Then The free body diagram of the satellite and astronaut in that satellite is as shown in the figure.

Let the satellite is moving with a speed V in a circular path of radius R. So, along with the satellite, the astronaut will also move. If m is the mass of the astronaut. Then the centrifugal force (Normal reaction) acts on him is,
FN = mV2R.
Here, the weight of the person is,
W = mg.
Then, Apparent weight of the astronaut is,
Wapp = W − FN
As we know, if the centrifugal acceleration of the satellite is less than that of the acceleration due to gravity, the satellite moves towards the earth and if the velocity increases, then the centrifugal force will become more than the acceleration due to gravity, then the satellite moves away from the earth.
So, here, both the centrifugal acceleration and the acceleration due to gravity are same, because the satellite is moving in a circular orbit of fixed radius.
Therefore, FN = Weight
So, Apparent weight is,
Wapp = W − FN ⇒ Wapp = 0.
So, astronaut feels weightless.
Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
When the satellite revolves in an orbit around the earth in a fixed orbit. Then The free body diagram of the satellite and astronaut in that satellite is as shown in the figure.

Let the satellite is moving with a speed V in a circular path of radius R. So, along with the satellite, the astronaut will also move. If m is the mass of the astronaut. Then the centrifugal force (Normal reaction) acts on him is,
FN = mV2R.
Here, the weight of the person is,
W = mg.
Then, Apparent weight of the astronaut is,
Wapp = W − FN
As we know, if the centrifugal acceleration of the satellite is less than that of the acceleration due to gravity, the satellite moves towards the earth and if the velocity increases, then the centrifugal force will become more than the acceleration due to gravity, then the satellite moves away from the earth.
So, here, both the centrifugal acceleration and the acceleration due to gravity are same, because the satellite is moving in a circular orbit of fixed radius.
Therefore, FN = Weight
So, Apparent weight is,
Wapp = W − FN ⇒ Wapp = 0.
So, astronaut feels weightless.
Hope this information will clear your doubts about the topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Answered by
1
HEYYA FRND. ..
When the satellite rotates in an orbit around the Earth then in a certain orbit. Then, in that satellite, the free body diagram of the satellite and astronauts is shown in the form of a picture.
The satellite should move with V speed in the circular path of radius R. So, along with the satellite, astronauts will also go forward if I have the mass of astronauts, then the centrifugal force (normal reaction) works on it,
.
Here is the weight of the person,
.
Then, the astronaut has a clear weight,
As we know, if the acceleration at the speed of the satellite due to gravity is less than the speed, then the satellite increases towards the Earth and if the velocity increases, the centrifugal force will be greater than the acceleration due to gravity, walks away
Therefore, here, due to gravity both centrifugal acceleration and acceleration are the same, because the satellite is running in the circular orbit of the defined radius.
Hence,
So, apparently weighing,
.
So, the astronaut feels weightless.
_________
THANK YOU
@SRK6
When the satellite rotates in an orbit around the Earth then in a certain orbit. Then, in that satellite, the free body diagram of the satellite and astronauts is shown in the form of a picture.
The satellite should move with V speed in the circular path of radius R. So, along with the satellite, astronauts will also go forward if I have the mass of astronauts, then the centrifugal force (normal reaction) works on it,
.
Here is the weight of the person,
.
Then, the astronaut has a clear weight,
As we know, if the acceleration at the speed of the satellite due to gravity is less than the speed, then the satellite increases towards the Earth and if the velocity increases, the centrifugal force will be greater than the acceleration due to gravity, walks away
Therefore, here, due to gravity both centrifugal acceleration and acceleration are the same, because the satellite is running in the circular orbit of the defined radius.
Hence,
So, apparently weighing,
.
So, the astronaut feels weightless.
_________
THANK YOU
@SRK6
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