## Excerpt

## NASA Preliminary Calculations

**Introduction**

A satellite can be thought as an object that orbits around a large body mass. Human-made satellites are launched into space with a purpose of communication, scientific research, weather forecasting, intelligence purpose among other broad applications. The motion of a satellite around a massive body is a projectile. Upon reaching the space, the only gravitational force acts upon the satellite. However, when launched at a sufficient speed, any satellite will orbit any large body. When launching satellites to orbit around the Mars, scientists have to determine the exact speed to launch the satellite so that it can remain on the orbit (Yvelyne 86). From the laws governing a projectile launched body, a satellite moves in a direction that is tangent to the Mars. As a result, the force of gravity of the Mars acts to pull it down. If the commence speed is too small, the launched body would fall to the Mars as the Mars’s gravitational forces would pull it down. When started with sufficient speed, the body would take a circular path and would fall to surface or Mars (Léonie, Léonie and Grady 13). When the launch speeds are made to be significantly large, the projected body moves at an elliptical path. At every point along the trajectory path, the satellite falls towards the surface of the Mars. However, it does not reach the surface of the Mars. For the case of this essay, the primary objective is to develop preliminary calculations. The scheming will show how high the satellite must be placed above the surface of the planet Mars and the speed that it must maintain while on the orbit.

**Laws**

The laws governing the motion of a satellite around the mars will be Newton's laws. The law of acceleration and Newton's form of Kepler's third law will be applicable in determining the relationship between the gravitational force acting on the planet and the period.

**Calculations**

For instance, considering the mass of planet Mars to be Abbildung in dieser Leseprobe nicht enthalten and the mars of the satellite to beAbbildung in dieser Leseprobe nicht enthalten, it is possible to customize Newton's gravitational laws to one that can be used for this problem. Planet Mars can be the central object while the satellite will revolve around the planet (Stephanie 75). Therefore, planet Mars will cause a sufficient acceleration on the satellite. Assuming that the satellite moves in a circular motion, centripetal forces will act upon the orbiting satellite and will be given by the relationship:

Abbildung in dieser Leseprobe nicht enthalten

This net force arises from the gravitational force that attracts the satellite towards the central body. The force of gravity will have the value:

Abbildung in dieser Leseprobe nicht enthalten

Since the force of gravity is equivalent to the net centripetal force, it is possible to combine the two equations to get:

Abbildung in dieser Leseprobe nicht enthalten

Since the mass of the satellite is present in both formulas, it cancels out to give rise to:

Abbildung in dieser Leseprobe nicht enthalten

The term R will also simplify to obtain:

Abbildung in dieser Leseprobe nicht enthalten

The above formula can be used to determine the speed required to launch the satellite so that it can revolve around Mars without falling.

Abbildung in dieser Leseprobe nicht enthalten

The above equation shows that the force of gravity is the only force that will determine the speed with which the satellite will revolve around the planet Mars. The gravitational force of planet Mars has the valueAbbildung in dieser Leseprobe nicht enthalten. The mass of planet Mars is Abbildung in dieser Leseprobe nicht enthalten (Stephanie, 34).

The gravitational law is not enough to explain the case of a satellite moving around mars. Other laws such as acceleration and Kepler's third law will be very applicable to this case. The mass and radius of planet Mars will help to determine the acceleration of the satellite. Since the only force acting on the moving satellite is the gravitational force, the magnitude of the acceleration will be equivalent to the acceleration by the gravity of the satellite at any particular location or instance ion location. Therefore:

Abbildung in dieser Leseprobe nicht enthalten

**[...]**

## Details

- Pages
- 8
- Year
- 2018
- ISBN (eBook)
- 9783668737358
- File size
- 596 KB
- Language
- English
- Catalog Number
- v429321
- Grade
- Tags
- nasa preliminary calculations