The force exerted by the earth on a particle of mass m a distance r from the

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The force exerted by the earth on a particle of mass m a distance r from the center of the earth has the magnitude GMEm/r2 = mgRE2/r2.

(a) Calculate the work you must do against gravity to move the particle from a distance r1 to r2.s

(b) Show that when r1 = RE and r2 = RE + h, the result can be written

W = mgR RE RĘ +h

(c) Show that when h << RE, the work is given approximately by W = mgh.

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