6.5 Newton’s Universal Law of Gravitation

Jupiter has a mass approximately 300 times greater than Earth's and a radius about 11 times greater. How will the gravitational acceleration at the surface of Jupiter compare to that at the surface of the Earth?

1. Greater
2. Less
3. About the same
4. Not enough information

In the formula $g = \frac{G M}{r^{2}}$, what does G represent?

1. The acceleration due to gravity
2. A gravitational constant that is the same everywhere in the universe
3. A gravitational constant that is inversely proportional to the radius
4. The factor by which you multiply the inertial mass to obtain the gravitational mass

A recently discovered planet has a mass twice as great as Earth's and a radius twice as large as Earth's. What will be the approximate size of its gravitational field?

1. 19 m/s²
2. 4.9 m/s²
3. 2.5 m/s²
4. 9.8 m/s²

Earth is not a perfect sphere. Its radius as well as the value of g vary with latitude. (a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is $9.807 m /\text{s}^{2}$ and the radius of the Earth at the pole is 6356.8 km.

(b) Compare this with the accepted value of $5.972 \times \text{10}^{\text{24}} \text{kg}$.

(a) What is the acceleration due to gravity on the surface of the Moon?

(b) On the surface of Mars? The mass of Mars is $6.418 \times \text{10}^{\text{23}} \text{kg}$ and its radius is $3 . \text{38} \times \text{10}^{6} \text{m}$.

The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the surface.)

(a) Calculate the magnitude of the acceleration due to the Moon’s gravity at that point.

(b) Calculate the magnitude of the centripetal acceleration of the center of Earth as it rotates about that point once each lunar month (about 27.3 d) and co…

(a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).

(b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some $6 . \text{29} \times \text{10}^{\text{11}} \text{m}$ away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in…

(a) The Sun orbits the Milky Way galaxy once each $2 . \text{60 x 10}^{8} \text{ y}$, with a roughly circular orbit averaging $3 . \text{00 x 10}^{4}$ light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun?

(b) Calculate the average speed of the Sun i…

Unreasonable Result

A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight.

(a) Calculate the mass of the mountain.

(b) Compare the mountain’s mass with that of Earth.

(c) What is unreasonable about these results?

(d) Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby…