Advertisements
Advertisements
Question
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
Solution
Given: m = 2000 kg, h = 3600 km = 3.6 × 106 m,
G = 6.67 × 10-11 Nm2/kg2,
R = 6400 km = 6.4 × 106 m,
M = 6 × 1024 kg
To find:
1. Kinetic energy (K.E.)
2. Potential energy (P.E.)
3. Total energy (T.E.)
4. Binding energy (B.E.)
Formulae:
1. K.E. = `"GMm"/(2("R + h"))`
2. P.E. = `- "GMm"/("R + h")` = - 2(K.E.)
3. T.E. = K.E. + P.E.
4. B.E. = –T.E.
Calculation:
From formula (i),
K.E. = `(6.67 xx 10^-11 xx 6 xx 10^24 xx 2 xx 10^3)/(2 xx [(6.4 xx 10^6) + (3.6 xx 10^6)])`
`= (6.67 xx 6 xx 10^16)/10^7`
= 40.02 × 109 J
From formula (ii),
P.E. = –2 × 40.02 × 109 = - 80.04 × 109 J
From formula (iii),
T.E. = (40.02 × 109) + (–80.04 × 109) = - 40.04 × 109 J
From formula (iv),
B.E. = – (–40.02 × 109) = 40.02 × 109 J
Kinetic energy of the satellite is 40.02 × 109 J potential energy is –80.04 × 109 J, total energy is -40.02 × 109 J and binding energy is 40.02 × 109 J.
APPEARS IN
RELATED QUESTIONS
Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east one to west and the other from west to east. Will they have the same time period as seen from the earth? If not which one will have less time period?
A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.
The time period of an earth-satellite in circular orbit is independent of
A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve. Its speed with respect to the satellite
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
(a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation. (b) If the satellite is directly above the North Pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth = 6 × 1024 kg.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
Find the minimum colatitude which can directly receive a signal from a geostationary satellite.
Answer the following question.
What do you mean by geostationary satellite?
Answer the following question in detail.
Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Solve the following problem.
Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
Solve the following problem.
What is the gravitational potential due to the Earth at a point which is at a height of 2RE above the surface of the Earth?
(Mass of the Earth is 6 × 1024 kg, radius of the Earth = 6400 km and G = 6.67 × 10–11 N m2 kg–2)
If a body weighing 40 kg is taken inside the earth to a depth to radius of the earth, then `1/8`th the weight of the body at that point is ______.
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 ____________.
Reason of weightlessness in a satellite is ____________.
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 ____________.
Out of following, the only correct statement about satellites 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
In the case of earth, mean radius is 'R', acceleration due to gravity on the surface is 'g', angular speed about its own axis is 'ω'. What will be the radius of the orbit of a geostationary satellite?
The period of revolution of a satellite is ______.
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.
Two satellites are orbiting around the earth in circular orbits of same radius. One of them is 10 times greater in mass than the other. Their period of revolutions are in the ratio ______.
Two satellites of same mass are orbiting round the earth at heights of r1 and r2 from the centre of earth. Their potential energies are in the ratio of ______.
