# Orbital period and speed of a space shuttle in flight

• kevnm67
In summary, the space shuttle, which is in a 290-mile-high orbit, has an orbital speed of approximately 7639.54 meters per second. The formula used to calculate this speed is v=√GM/R+h, where G is the gravitational constant, M is the mass of the Earth, R is the radius of the Earth, and h is the altitude of the orbit. The calculated period of the shuttle's orbit is approximately 5622.8 seconds.
kevnm67

## Homework Statement

The space shuttle is in a 290-mile-high orbit. What is the shuttles orbital speed?

v=√GM/R+h

## The Attempt at a Solution

Period:
Me= 5.98x10^24kg
Re= 6.38x10^6m
H= 290miles * 1609m = 466610m

v= √(6.67x10^-11 N)(5.98x10^24 kg)/ (6.38x10^6 m)+ 466610 m

I didn't get the correct answer and would like some help working through this problem.

try

$$v = \sqrt {\frac{ G M } {R+h}}$$

That's the equation I used above

i don't know if this is correct but here are my recent calculations:

v=2pi r/T ---> 42955687.5/T
G*M/r^2 = 8.5368*r= 58362553.54 ->v=sqrt(58362553.54)= 7639.54
T=2pi r/v = 5622.8

To calculate the orbital speed of the space shuttle, we can use the equation v=√GM/R+h, where G is the gravitational constant, M is the mass of the Earth, R is the distance from the center of the Earth to the object's orbit, and h is the height of the orbit.

In this case, we can assume that the shuttle's orbit is circular, so R is equal to the sum of the radius of the Earth (Re) and the height of the orbit (h). Plugging in the values, we get:

v=√(6.67x10^-11 N)(5.98x10^24 kg)/ (6.38x10^6 m + 466610 m)

= 7.68 km/s

Therefore, the orbital speed of the space shuttle in this scenario is approximately 7.68 km/s. It is important to note that this is an average speed and the actual speed may vary slightly due to factors such as atmospheric drag and changes in the shuttle's altitude.

## 1. What is the orbital period of a space shuttle in flight?

The orbital period of a space shuttle in flight is the time it takes for the shuttle to complete one full orbit around the Earth. This is typically around 90 minutes.

## 2. How is the orbital period of a space shuttle determined?

The orbital period of a space shuttle is determined by its altitude and velocity. The higher the altitude and faster the velocity, the longer the orbital period will be.

## 3. What is the average speed of a space shuttle in orbit?

The average speed of a space shuttle in orbit is approximately 17,500 miles per hour. This is necessary to maintain a stable orbit around the Earth.

## 4. How does the speed of a space shuttle change during its orbit?

The speed of a space shuttle changes constantly during its orbit. As it gets closer to the Earth, its speed increases due to the gravitational pull, and as it moves further away, its speed decreases. This is known as orbital velocity.

## 5. Can the orbital period and speed of a space shuttle be changed?

Yes, the orbital period and speed of a space shuttle can be changed by adjusting its altitude and velocity. This is often done to perform specific tasks or maneuvers in space.

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