View the step-by-step solution to:

# [DEFAULT] BASEURL=https://www.aerospacescholars.org/as/mod/assign/view.php?

Shuttle Math

Why do astronauts float? Is it because there is no gravity in outer space? If there is gravity in outerspace, how does it compare to gravity here on Earth's surface?

On the Space Shuttle, the gravitational status of astronauts is often described as a "Zero-g" environment. The symbol “g” refers to the acceleration all objects at Earth’s surface experience as a result of Earth’s gravitational force and is given a value of 1 g, or described as an acceleration of 9.81 m/s2 towards the Earth. Forces cause acceleration; if astronauts were in a true zero-g environment they would experience no gravitational acceleration. This would mean they do not experience a gravitational force either; this, however, is not true!

Every object with mass in the universe exerts a gravitational pull on every other object with mass.

Every single object, all of them, acts on every other object! There are ways to simplify this, however, and most physics is done with these simplifications in mind: The more massive the object, the stronger the gravitational attraction. The closer the objects are to each other, the stronger the attraction. The opposite is true as well, as the distance between the astronauts and Earth’s center increases, the gravitational pull between the astronaut and the Earth decreases.

Sir Isaac Newton realized that the same force that caused apples to fall from trees was responsible for holding the Moon in orbit around Earth (and the shuttle around the Earth). He also realized that as the distance grows between two objects the attraction drops, but most importantly, it never reaches zero! These ideas are expressed mathematically in an equation, Newton's Law of Gravitation, that will be given in Module 6’s math problem.

So how does the gravity of Earth affect a spacecraft in orbit? The magnitude of the gravitational pull of Earth on the Shuttle astronauts is very close to the same as the gravitational force holding you in chair. "But wait", you say, "the astronauts are floating, and I'm not!"

True, the astronauts are experiencing weightlessness, but they are not experiencing a true zero-g environment or zero pull from Earth's gravity. As objects increase in altitude and move away from Earth’s surface, they will experience less of Earth’s gravitational force and will have a lesser acceleration when they are allowed to fall back to earth. But the force does not become zero and the reduction in force alone is not sufficient to cause weightlessness.

The astronauts are experiencing weightlessness because they are perpetually in free fall.

Isaac Newton realized that gravity's effects on objects could also be described in terms of falling. If you threw a baseball directly towards the horizon it would travel forever if it were not being acted upon by gravity and frictional air resistance. Gravity causes the ball to fall back to Earth in an arc. If you throw the ball harder, it will travel farther, but it will still fall in an arc. If you throw it really hard or launch it via a cannon, the ball could travel so fast that as it arcs towards the surface of the Earth, the curvature of the Earth matches the curvature of the arc.
The ball would be continually arcing towards a surface that is continually arcing out of its way, and this is the most basic type of Orbit. For an interactive version of Newton's cannon on a mountain, click here!

The speed necessary to reach this situation on Earth is about 28,200 kilometers per hour (17,500 miles per hour) and this is the speed that the Space Shuttle must attain to continue to "fall" around Earth (remain in orbit) at an altitude of 300 kilometers (186 miles). To fully "escape" the Earth's gravitational force, you have to go even faster than that. The "escape velocity" for the Earth is about 40,300 kilometers per hour, or about 25,000 miles per hour.

Please calculate the percent of Earth’s gravitational force on the Shuttle astronauts while orbiting at an altitude of 248 miles (or 399 km) above Earth’s surface. To do this, compare the gravitational force on an orbiting astronaut to the force on the astronaut here at Earth’s surface using the following equation the astronaut here at Earth’s surface using the following equation:
[DEFAULT] BASEURL=https://www.aerospacescholars.org/as/mod/assign/view.php?id=983 [{000214A0-0000-0000-C000-000000000046}] Prop3=19,11 [InternetShortcut] URL=https://www.aerospacescholars.org/as/pluginfile.php/1760/mod_assign/intro/Mo dule_3/Shuttle_Math/Graviaty_Comparison_Equation.png IDList= IconFile=https://www.aerospacescholars.org/as/theme/image.php/_s/rocket/theme/13 56811479/favicon IconIndex=1

### Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

### -

Educational Resources
• ### -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

Browse Documents