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प्रश्न
Solve the problem.
How much time a satellite in an orbit at height 35780 km above earth's surface would take, if the mass of the earth would have been four times its original mass?
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उत्तर
Given:
Height of the satellite, h = 35780 km
Let the original mass of Earth be M. Then its new mass will be 4M.
The time taken by the satellite to revolve around the Earth's orbit is given as
`T = (2piR)/(v_c)`
Now, vc is given as
`v_c = sqrt((GM)/(R + h))`
Thus,
`T = (2pi(R + h))/(sqrt((GM)/(R + h))) = (2pi(R + h)sqrt(R + h))/(sqrt(GM))` ...(i)
= `T propto 1/(sqrt(M))` ...(ii)
Thus, from equation (ii), we see that when the mass of the Earth becomes 4 times, the time period of revolution of the satellite should be halved.
i.e., `T_(4M) = T/2` ...(iii)
Now, h = 35780 km
M = 6 × 1024 kg
R = 6.4 × 105 m
G = 6.67 × 10−11 N m2/kg2
Putting the values of h, M and R first, we get
T = 24 h
Using (iii), we get
`T_(4M) = 24/2 = 12`h
संबंधित प्रश्न
Answer the question:
What is meant by the orbit of a satellite? On what basis and how are the orbits of artificial satellites classified?
Why are geostationary satellites not useful for studies of polar regions?
Mahendra and Virat are sitting at a distance of 1 metre from each other. Their masses are 75 kg and 80 kg respectively. What is the gravitational force between them? G = 6.67 x 10-11 Nm2/kg2
A group of students from COEP Pune sent a small satellite _______ through ISRO in 2016.
Distinguish between:
High Earth orbit - Medium Earth orbit.
Observe the figure and write the answers.
- Name the outer orbit.
- Which satellites revolve in low earth orbits?
- Which various orbits are given in the figure?
- Give an example of a launch vehicle based on Newton’s third law.
Write functions of Military satellite and Navigational satellite.
Note the relationship between the entries in all the three columns in the table and rewrite the table.
| Column-1 (Location) |
Column-2 Height from the earth’s surface (km) |
Column-3 g (m/s2) |
| Earth’s surface (average) | 8.8 | 0.225 |
| Mount Everest | 36.6 | 9.81 |
| Maximum height ever reached by manmade balloon | 400 | 9.8 |
| Orbit of a typical weather satellite | 35700 | 9.77 |
| Orbit of communication satellite | 0 | 8.7 |
Define orbital velocity.
How is a satellite maintained in nearly circular orbit?
Write down the formula of orbital velocity.
Give scientific reasons.
The geostationary satellite is not useful in the study of polar regions.
Geostationary satellites are not useful for studies of the polar region.
The height of medium earth orbit above the surface of the earth is ______.
Write the name of small satellite made by a group of students from COEP (College of Engineering, Pune) sent to the space through ISRO in 2016.
Complete the following equations:
The orbit of a satellite is exactly 35780 km above the earth's surface and its tangential velocity is 3.08 km/s.
How much time the satellite will take to complete one revolution around the earth?
(Radius of earth = 6400 km.)
