Answer:
a) g = moon = - 3,329 10⁻⁵ m / s², b)g_sum = - 5,934 10⁻³ m / s²
c) g_sum / g_moon = 1.78 10²
Explanation:
a) From the law of universal gravitation, the gravitational field is
F = - G M m / r²
the gravitational field is
g = F / m
g = - G M / r²
let's calculate this field the Earth and the Moon
g_moon = - G M_moon / r²
M_moon = 7.36 10²² kg
r = 3.84 10⁸ m
let's calculate
g_moon = - 6.67 10⁻¹¹ 7.36 10²² / (3.84 10⁸)²
g = moon = - 3,329 10⁻⁵ m / s²
B) let's calculate the field of the sun in the position of the Earth
M = 1,991 10³⁰ kg
r = 1,496 10¹¹ m
g_ Sun = - 6.67 10⁻¹¹ 1,991 10³⁰ / (1,496 10¹¹)²
g_sum = - 5,934 10⁻³ m / s²
c) the relationship between the two gravitational fields is
g_sun / g_moon = 5,934 10⁻³ / 3,329 10⁻⁵
g_sum / g_moon = 1.78 10²