Question

which of the following statements about the effects of gravity are true?
select all that apply
a you and your desk attract each other with the same force of gravity as earth attracts you.
b objects that are closer together have a weaker force of gravity between them.
c the force of gravity is greater between the moon and the sun than between the moon and earth.
d objects with greater mass have a stronger force of gravity between them.
e the moon circles around earth rather than the sun because the force of gravity is greater between the moon and earth.

Explanation:

Step1: Analyze option a

According to Newton's third law, the force of gravity between two objects is mutual. But the force of gravity between you and the desk \(F_{1}=G\frac{m_{you}m_{desk}}{r^{2}}\), and the force of gravity between you and the Earth \(F_{2}=G\frac{m_{you}m_{Earth}}{r'^{2}}\). Since \(m_{Earth}\gg m_{desk}\), \(F_{1}
eq F_{2}\). So option a is false.

Step2: Analyze option b

The formula for the gravitational force is \(F = G\frac{m_{1}m_{2}}{r^{2}}\), where \(G\) is the gravitational constant, \(m_{1}\) and \(m_{2}\) are the masses of the two objects, and \(r\) is the distance between them. When \(r\) decreases (objects are closer), \(F\) increases. So option b is false.

Step3: Analyze option c

The mass of the Sun \(M_{sun}\approx1.989\times 10^{30}\space kg\), the mass of the Earth \(M_{earth}\approx5.972\times 10^{24}\space kg\), the mass of the Moon \(M_{moon}\approx7.348\times 10^{22}\space kg\). The distance between the Moon and the Sun \(r_{sun - moon}\) and the distance between the Moon and the Earth \(r_{earth - moon}\). Using \(F = G\frac{m_{1}m_{2}}{r^{2}}\), \(F_{sun - moon}=G\frac{M_{sun}M_{moon}}{r_{sun - moon}^{2}}\), \(F_{earth - moon}=G\frac{M_{earth}M_{moon}}{r_{earth - moon}^{2}}\). Although \(M_{sun}\gg M_{earth}\), \(r_{sun - moon}\gg r_{earth - moon}\). In fact, \(F_{sun - moon}\approx2F_{earth - moon}\). So option c is true.

Step4: Analyze option d

From \(F = G\frac{m_{1}m_{2}}{r^{2}}\), when \(r\) is constant, if \(m_{1}\) or \(m_{2}\) increases, \(F\) increases. So objects with greater mass have a stronger force of gravity between them (when the distance is fixed). Option d is true.

Step5: Analyze option e

As calculated in step 3, \(F_{sun - moon}\approx2F_{earth - moon}\). But the Moon circles around the Earth because of the combination of the gravitational force and the initial velocity of the Moon. The net - effect of gravitational forces and the orbital motion make the Moon orbit the Earth. So option e is false.

Answer:

C. The force of gravity is greater between the moon and the sun than between the moon and Earth; D. Objects with greater mass have a stronger force of gravity between them.