Ch#5: Gravitation Flashcards
Learn about gravitation, mass of the earth and satellites.
State and explain the law of gravitation with diagram(fig. 5.1)
Definition : Everybody in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of distance between their centres.
Consider two bodies of masses m1 and m2. The distance between the centre of the bodies is d. According to law of gravitation: F > m1 m2 F > 1/d² F > m1 m2/d² F = G m1 m2/d²
G is the propertionality constant , it is universal constant of gravitation. In SI Units its value is 6.673 x 10^-11N/m²kg².
Due to the small value of G , we dont feel the force of gravitation between objects around us. The earth attracts object with significant force due to its large mass.
How are the law of gravitation and 3rd law of motion related?
It is to be noted that mass m1 attracts m2 towards it with a force F while mass m2 attracts m1 towards it with force of same magnitude and opposite direction. If the force acting on m1 is considered action then the force acting on m2 is considered reaction. The action and reaction due to force of gravitation are equal in magnitude but opposite in direction. This is consistent with Newton’s 3rd law which states :
“To every action there is an equal but opposite reaction”
Describe the gravitational force , field force and gravitional field strength.
The gravitational force between a bidy of mass m and the earth is given by:
F = G m1 Me/r²
Me is the mass of the earth and r is the distance of the body from the centre of the earth.The weight of a body is due to the gravitational force with which the earth attracts objects.
Gravitional force is a non contact force. for instance , the velocity of a body thrown vertically upwards decreases. This is due to the gravitational pull of the earth acting on the body whether the body is in contact with the earth or not. Such a force is called a field force. It is assumed a gravitional field exists all around the world. This field is directed towards the centre of the earth.
The gravitational field becomes weaker as we move further away fron the earth. In the gravitational field of the earth z the gravitational force per unit mass is called the gravitational field strength of the earth. At any place , it is equal to g. Near the surface of the earth , it is 10 N/Kg
Explain and derive the mass of the earth.
Consider a body of mass m on the surface of the earth. Let the mass of the earth be Me and the radius of the earth be R. The distance of the body from the centre of the earth will be equal to radius R of the earth. According to the law of gravitation , the gravitional force F is given by :
F = G m Me/R²
But the force with which the earth attracts a body towards its centre is equal to its weight. F = w = mg mg = G m Me/R² g = G Me/R² Me = R²g/G
mass Me can be obtained by putting in the values.
Me = (6400000m)² x 10ms /6.673 x 10^-11 N/m²kg²
Me = 6 x 10^24kg.
Explain the variation of g with altitude. What happens to g if we go 1 or 2 earth radius above the earth?
The Equation (g = G Me/R²) shows that the value of gravitation acceleration g depends on the radius of the earth. The value of g is inversely proportional to the square of the distance from the centee of the earth. The value of g is not constant , it decreases with the increase in altitude. Altitude is the height of an object or place above sea level. The value of g is greater at sea level than at the hills.
Consider a body of mass m at altitude h. The distance of the body from the centre of the earth will be R + h. Therefore , using the earlier equation:
gh = G Me/(R + h)²
Using that equation , we find that the value of g at one earth radius above the earth is 1/4th of its value on the earth’s surface. At a distance of 2 earth radius above the earth’s surface , the value of g becomes 1/9th of its value on the earth’s surface.
Explain artificial satelites and the orbits of communication satelites.
An object which revolves around the earth is called a satelite. The moon revolves around the Earth so the moon is a natural satelite of the earth. Scientists have sent many objects into space. Some of these objects revolve around the Earth. These are called artificial satelites. Most artificial satelites revolving around the earth are used for communication purposes. Artificial Satelites carry instruments and passengers to perform experiments in space.
A large of artificial satelites have been launched in different orbits around the earth. They take different times to complete a revolution around the earth depending on the distance h from the earth. Communication satelites take 24hours to complete a revolution around the earth.The earth completes a rotation in 24hours so these satelites appear to be stationary with respect to earth. Due to this reason ,the orbit of such satelites are called geostationary orbits. Dish antennas sending and receiving signals from them have fixed direction depending on their location on the earth.
State and explain the motion of artificial satelites.Also make an approximation for a satelite revolving close to the earth.
A satelite requires centripetal force that keeps it moving in a orbit around the earth. The gravitational force of attraction between the satelite and the earth provides the necessary centripetal force.
Consider a satelite of mass m revolving around the jucleas at altitude h in an orbit of radius Ró with orbital velocity Vo. The necessary centripetal force is given by:
Fc = mv²/Ro
This force is provided by the gravitational force of attraction between the satelite and the earth and is equal to the weight w’ of the satelite.
Fc = w’ = m gh
or mgh = mv²/r Vo² =gh Ró Vo = √gh Ro As Ro = R + h Vo = √gh (R+h) ---(i)
Equation (i) gives the velocity which a satelite must possess when launched in an orbit of radius Ro. An approximation can be made for a satekite revolving close to the earth’s surface.
R + h ≈ R
gh ≈ g
Vo = √g R
A satelite revolving close to the earth’s surface has speed Vo of nearly 8km/s or 29000hm/h.
