Question

Use Newton's law of universal Gravitation to estimate force exerted by one object on another: F = G m_1 m_2/r^2 In which m_1 and m_2 are masses of object 1 and 2 in kg, and r is the distance between the two in meters. G is universal gravitational constant equal to 6.673 * 10^-11 Nm ^2/kg^2. What is the force that moon (m_l = 7.4 * 10^22 kg) exerts to earth (m_2 = 6 * 10^24 kg) knowing that they are 3 * 10^8 m apart? What is the unit of force? MATLAB allows for logarithm calculations at the base of 2, 10 and natural logarithm (log2, logl0, and log). However, you can use logarithm base change rule log_b(x) = log_c (x)/log_c (b) to calculate log at any base. Calculate the following: log_3(50) log_8(90) log_4(50) log_30(50)

Answer 1

G = 6.673e-11;

m1 = 7.4e22;
m2 = 6e24;

r = 3e8;

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

Unit of Force is Newton

8

a = log(50)/log(3)

b = log(90)/log(8)

c = log(50)/log(4)

d = log(50)/log(30)

Answer:

a =  3.5609                                                                                                                                                              

b =  2.1640                                                                                                                                                              

c =  2.8219                                                                                                                                                              

d =  1.1502