Advertisements
Advertisements
Question
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Advertisements
Solution
The expression for critical velocity:
- Consider a satellite of mass m revolving round the Earth at height h above its surface. Let M be the mass of the Earth and R be its radius.
- If the satellite is moving in a circular orbit of radius (R + h) = r, its speed must be equal to the magnitude of critical velocity vc.
- The centripetal force necessary for the circular motion of a satellite is provided by the gravitational force exerted by the satellite on the Earth.
∴ Centripetal force = Gravitational force
∴ `("mv"_"c"^2)/"r" = "GMm"/"r"^2`
∴ `"v"_"c"^2 = "GM"/"r"`
∴ `"v"_"c" = sqrt("GM"/"r")`
∴ `"v"_"c" = sqrt("GM"/("R + h")) = sqrt("g"_"h" ("R + h"))`
This is the expression for critical speed at the orbit of radius (R + h). - The critical speed of a satellite is independent of the mass of the satellite. It depends upon the mass of the Earth and the height at which the satellite is the revolving or gravitational acceleration at that altitude.
APPEARS IN
RELATED QUESTIONS
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000 km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
The time period of an earth-satellite in circular orbit is independent of
Choose the correct option.
The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 109 J. It's kinetic energy is ______.
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
What is periodic time of a geostationary satellite?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth.
Given: G = 6.67 × 10-11 Nm2/kg2
R = 6400 km, M = 6 × 1024 kg
Answer the following question in detail.
Two satellites A and B are revolving round a planet. Their periods of revolution are 1 hour and 8 hour respectively. The radius of orbit of satellite B is 4 × 104 km. Find radius of orbit of satellite A.
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
Solve the following problem.
Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
Two satellites of a planet have periods of 32 days and 256 days. If the radius of the orbit of the former is R, the orbital radius of the Latter is ______
What is the minimum energy required to launch a satellite of mass 'm' from the surface of the earth of mass 'M' and radius 'R' at an altitude 2R?
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3v, the speed of satellite B is ____________.
If the Earth-Sun distance is held constant and the mass of the Sun is doubled, then the period of revolution of the earth around the Sun will change to ____________.
Two satellites of masses m and 4m orbit the earth in circular orbits of radii 8r and r respectively. The ratio of their orbital speeds is ____________.
If a body weighing 40 kg-wt is taken inside the earth to a depth to `1/2` th radius of the earth, then the weight of the body at that point is ____________.
The ratio of energy required to raise a satellite to a height `(2R)/3` above earth's surface to that required to put it into the orbit at the same height is ______.
R = radius of the earth
A satellite is to revolve round the earth in a circle of radius 9600 km. The speed with which this satellite be projected into an orbit, will be ______.
A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.
Is it possibe for a body to have inertia but no weight?
Show the nature of the following graph for a satellite orbiting the earth.
- KE vs orbital radius R
- PE vs orbital radius R
- TE vs orbital radius R.
An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface ______ km/s.
[g = 9.8 ms-2 and Re = 6400 km]
The ratio of binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height h above the earth's surface is ______ (R = radius of the earth).
A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.
(G = universal constant of gravitation)
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
What is the typical altitude range for a polar satellite's orbit?
Which of the following is an example of a communication (geostationary) satellite launched by India?
