3) [S pts] Newton\'s law of universal gravitation is given by Gm1m2 2 Where F: F

Question

3) [S pts] Newton's law of universal gravitation is given by Gm1m2 2 Where F: Force of gravitational attraction G: universal gravitational constant 6.673 x 10-11 N m2/kg2 mi: mass of object 1 (kg) m2 : mass of object 2 (kg) r: distance between the objects' centers (m) a) Solve the above equation for m b) Suppose a student is in an airplane at 6.39 x 10° m above the earth's center. If the force of gravitational attraction between the earth and the 70-kg student is 684 N find the mass mi of the earth using subs' command.

Explanation / Answer

a) syms F m1 m2 G r %kind of defining symbolic variable

eq1 = F == (G * m1 * m2) / (r*r);

eq1 = isolate(eq1,m1) % isolate function will solve equation for m1

o/p = eq1 =

m1 == F*r^2/G*m2

b) subs(m1 == (r*r*F)/(m2*G), [r, F, m2, G], [6.39e+6, 684, 70, 6.673e-11]);

Explaination: subs stands for symbolic substitution. its syntax is

subs(s,old,new)

returns a copy of s, replacing all occurrences of old with new, and then evaluates s.

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