Physics

Problem

An experimental probe measures the acceleration due to gravity to be

6.5\,\text{m}\,\text{s}^{-2}

at an altitude of

1000\,\text{km}

above the Earth’s surface. Take the standard value of

g

at the surface to be

9.8\,\text{m}\,\text{s}^{-2}

. a. (i) Establish a relation connecting the acceleration due to gravity

g_{h}

at height

h

with the Earth’s radius

R

and the surface value of

g

. b. (ii) Using the given numerical data, determine the radius of the Earth. c. (iii) With your calculated value of

R

, estimate the escape speed from the Earth’s surface.