In , NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of and a radius of
a. What is the speed of a satellite orbiting above the surface?
b. What is the escape speed from the asteroid?
a. The speed of the satellite is
b. The escape speed from the asteroid is
Height = mass of asteroid (M) = , Radius of asteroid (R) =
For a satellite to revolve around the planet the necessary centripetal force is provided by the gravitational force of attraction between the planet and the satellite.
Where orbital radius of satellite r = R + h
Substituting values and solving we get : .
The speed of the satellite is
Mass of the asteroid (M) = radius of asteroid =
The escape speed from a planet is given by the formula :
Substituting values in the formula we get :
The escape speed from the planet is
A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + Δr, where Δr << r , has the very slightly different period T+ ΔT.
a) Show that
b) Two earth satellites are in parallel orbits with radii 6700 km and 6701 km. One day they pass each other, 1 km apart, along a line radially outward from the earth. How long will it be until they are again 1 km apart?
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