A satellite orbits the earth at a height of `3.6xx10^(6)m` from its surface. Compute it’s a kinetic energy, b. potential energy, c. total energy. Mass of the satellite `=500kg` mass of the earth `=6xx10^(24)`kg, radius of the earth `=6.4xx10^(6), G=6.67xx10^(-11)Nm^(2)kg^(-2)`.
Text Solution
Verified by Experts
Here `r=R+h=6.4xx10^(6)+3.6xx10^(6)=10^(7)m` Orbital velocity of the satellite around the earth is given by `v_(0)=sqrt((GM)/((R+h)))=sqrt((6.67xx10^(-11)xx6xx10^(24))/(10^(7)))` `=sqrt(6.67xx6xx10^(6))ms^(-1)` a. `KE` of the satellite `=1/2mv_(0)^(2)` `=1/2xx500xx6.67x6xx10^()6=10^(10)J` b. `PE` of the satellite `=-(GMm)/(R+H)` `=-(6.67xx10^(-11)xx(6xx10^(24))xx500)/(10^(7))` `=-2xx10^(10)J` c. Total energy `=KE+PE=10^(10)-2xx10^(10)=-10^(10)J`
Topper's Solved these Questions
GRAVITATION
CENGAGE PHYSICS|Exercise Exercise 6.1|13 Videos
GRAVITATION
CENGAGE PHYSICS|Exercise Exercise 6.2|15 Videos
FLUID MECHANICS
CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos
KINEMATICS-1
CENGAGE PHYSICS|Exercise Integer|9 Videos
Similar Questions
Explore conceptually related problems
A satellite orbits the earth at a height of 500 km from its surface. Compute its (i) Kinetic energy, (ii) potential energy, and (iii) total energy. Mass of the satellite=300 kg, Mass of the earth= 6.0xx10^(24) kg, radius of the earth= 6.4xx10^(6) m, G= 6.67xx10^(-11)Nm^(2)Kg^(-2) . Will your answer alter if the earth were to shrink suddenly to half its size?
If a spaceship orbits the earth at a height of 500 km from its surface, then determine its (i) kinetic energy, (ii) potential energy, and (iii) total energy (iv) binding energy. Mass of the satellite = 300 kg, Mass of the earth = 6xx10^(24) kg , radius of the earth = 6.4 xx 10^(6) m, G=6.67 xx 10^(-11) "N-m"^(2) kg^(-2) . Will your answer alter if the earth were to shrink suddenly to half its size ?
A satellite orbits the earth at a height of 400 km, above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence ? Mass of the satellite=200 kg, mass of the earth= 6.0xx10^(24) kg, radius of the earth= 6.4xx10(6) m, G= 6.67xx10^(-11)Nm^(2)Kg^(-2) .
A satellite orbits the earth at a height of 400km above the surface. How much energy must be expanded to rocket the satellite out of the gravitational influence of earth? Mass of the satellite is 200kg, mass of earth =6.0 xx 10^(24) kg, radius of earth =6.4 xx 10^6 m , G=6.67xx10^(-11)Nm^2 kg^(-2).
Calculate the mass of sum if the mean radius of the earth's orbit is 1.5xx10^(8)km and G=6.67xx10^(-11)Nxxm^(2)//kg^(2)
A geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth's gravity at the site of the satellite ? Mass of the earth= 6xx10^(24) kg and radius =6400 km.
Find the escape velocity of a body from the earth. [M (earth ) = 6 xx 10^(24) kg, R ( earth) = 6.4 xx 10^(6) m. G = 6.67 xx 10^(-11) N.m^(2)//kg^(2)]
Find the gravitational potential energy of a body of mass 10 kg when it is on the earth's surface. [M(earth) =6xx10^(24)kg,"R (earth)"=6.4xx10^(6)m, G=6.67xx10^(-11)N.m^(2)//kg^(2)]
Determine the binding energy of satellite of mass 1000 kg revolving in a circular orbit around the Earth when it is close to the surface of Earth. Hence find kinetic energy and potential energy of the satellite. [Mass of Earth =6xx10^(24)kg , radius of Earth =6400km , gravitational constant G=6.67xx10^(-11)Nm^(2)//kg^(2) ]
