The Newtonian Gravitational force acting on object 1 caused by object 2 is given by: $$\vec{F}_{grav} = -G\dfrac{m_1 m_2}{|\vec{r}|^2}\hat{r}$$

1. What is $\vec{r}$? Draw this.
2. What is the direction of $\vec{F}_{grav}$?
3. If an object is moving in a circle with constant speed, is there a non-zero net force? If there is a non-zero net force, what is its direction?
4. A geosynchronous orbit is an orbit in which the object (satellite) matches the rotational period of the Earth. How long does it take a satellite in a geosynchronous orbit to complete one orbit?
5. A geostationary orbit is a special type of a geosynchronous orbit in which the orbiting object does not move from its position in the sky as observed from Earth's surface. Sketch an object in a geosynchronous orbit(but not a geostationary orbit), and also sketch an object in a geostationary orbit clearly indicating where the object is relative to a person on Earth at two different times in this orbit.

The Carver Media Group is planning the launch of a new communications satellite. Elliot Carver (head of Carver Media Group) is concerned about the launch. This is a $200,000,000 endeavor. In particular, he is worried about the orbital speed necessary to maintain the satellite's geostationary orbit (and if that depends on the launch mass). You were hired as an engineer on the launch team. Carver has asked that you allay his concerns.

1. How do you know you can classify the satellite's orbit as uniform circular motion?
2. If the gravitational force is acting inward, why does the satellite not fall to Earth?
3. What is the difference between the gravitational force, the net force, and the centripetal force ($mv^2/r$) in this case?
4. Is there a force exerted on Earth? If so, why do we ignore it? If not, why not?
5. Explain the difference between mass and weight.
6. Did your result make sense? Why or why not?

On a single graph, plot both the x-component of the satellite's momentum and the x-component of the net force acting on the satellite.