Conceptual Questions

Is the earth’s gravitational force on the sun larger than, smaller than, or equal to the sun’s gravitational force on the earth? Explain.

The gravitational force of a star on orbiting planet 1 is $F_1$. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force $F_2$. What is the ratio $F_1\text{/}{F}_2?$

A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.

1. What is the ratio $F_1\text{/}{F}_2$ of the gravitational force on the first satellite to that on the second satellite?

2. What is the ratio $a_1\text{/}{a}_2$ of the acceleration of the first satellite to that of the second satellite?

How far away from the earth must an orbiting spacecraft be for the astronauts inside to be weightless? Explain.

A space station astronaut is working outside the station as it orbits the earth. If he drops a hammer, will it fall to earth? Explain why or why not.

The free-fall acceleration at the surface of planet 1 is $20{\text{m/s}}^2$. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2?

Why is the gravitational potential energy of two masses negative? Note that saying “because that’s what the equation gives” is not an explanation.

The escape speed from Planet X is $10\text{,}000\text{m}\text{/}\text{s}$. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?

The mass of Jupiter is 300 times the mass of the earth. Jupiter orbits the sun with $T_{\text{Jupiter}}=11.9\text{years}$ in an orbit with $r_{\text{Jupiter}}=5.2r_{\text{earth}}$. Suppose the earth could be moved to the distance of Jupiter and placed in a circular orbit around the sun. Which of the following describes the earth’s new period? Explain.

1. 1 year

2. Between 1 year and 11.9 years

3. 11.9 years

4. More than 11.9 years

5. It would depend on the earth’s speed.

6. It’s impossible for a planet of earth’s mass to orbit at the distance of Jupiter.

Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.