Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

A spaceship is launched into a circular orbit close to the Earth’s surface. What additional velocity has to be imparted to the spaceship in the orbit to

overcome the gravitational pull? (R = 6400 km, g = 9.8 m/s²)

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

The energy of a satellite when it is stationary on the ground is due to rotation of Earth about itself and potential energy. Let Earth rotate about itself with angular velocity of w₀. Let the satellite be launched vertical to the surface of Earth.

Energy on the surface = 1/2 m R² w₀² - G M m / R --- (1)

When the satellite is revolving around the Earth in uniform circular motion at an altitude of h:

centripetal force = gravitational force m v² / (R+h) = G M m / (R+h)² m v² = G M m /(R+h)

Total energy of satellite = K E + P E = 1/2 m v² - G M m / (R+h) = - G M m / 2(R+h) --- (2)

Required kinetic energy = G M m [1/ R - 1/2(R+h) ] - 1/2 m R² w₀² E = (G M m/2R) * [1 + 2 h / (R+h)] - 1/2 m R² w₀²

we know g = G M /R² and let us assume h << R w₀ = 2π /86400 rad/sec

E = m R/2 * [ g - R w₀² ]

Substitute the values to get answer as a numerical value.