Question

Earth's orbit around the sun is not perfectly circular. The nearest point of its orbit is 1.471E8 kilometers. The mass of the sun is 1.989E30 kilograms. The mass of the earth is 5.97E24 kilograms. The universal gravitational constant is 6.6738E-11 N(m/kg)2. (a) What is the force exerted by the sun on the earth they are closest together? (b) What is the corresponding force of the earth on the sun?

Answer 1

Answer:

a) -3.66233E22 N

b) 3.66233E22 N

Explanation:

Closest distance between Earth and Sun = 1.471E8 kilometers = r

Mass of Earth = 5.97E24 kilograms = m

Mass of the sun = 1.989E30 kilograms = M

a) Universal gravitational constant = 6.6738E-11 N(m/kg)2

$F_{Mm}=-G\frac{Mm}{r^2}\\\Rightarrow F=-6.6738E-11 N \frac{5.97E24\times 1.989E30}{(1.471E11)^2}\\\Rightarrow F=-3.66233E22\ N$

Force exerted by the sun on the earth they are closest together is -3.66233E22 N

b) The magnitude of the force that the earth will exert on the sun will be same but the direction will be different represented by the change of the sign

$F_{mM}=-F_{Mm}\\\Rightarrow F_{mM}=-(-3.66233E22\ N)\\\Rightarrow F_{mM}=3.66233E22\ N$

Force exerted by the earth on the sun when they are closest together is 3.66233E22 N.