# Sattelite orbiting mars, work done to change distance.

• mark_dollar
In summary, the question asks how much work is needed for a 2700 kg spacecraft in a circular orbit 1000 km above the surface of Mars to move to a circular orbit 4000 km above the surface. Using the equations for total mechanical energy and kinetic energy, it can be determined that the work required is 5.33 x 10^9 J. There was initially some confusion due to incorrect equations and calculations, but the correct answer was eventually obtained.
mark_dollar

## Homework Statement

A 2700 kg spacecraft is in a circular orbit 1000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

## Homework Equations

TME=U+KE
U=Gm1m2/R
KE=.5Gm1m2/r (this doesn't seem right for some reason)

## The Attempt at a Solution

U1+k1+work=U2+k2
work=U2+k2-(u1+k1)
u1=2.630*10^10
ke1=1.315*10^10
U2=2.891*10^10
Ke2=1.446*10^10
TME1=3.945*10^10
TME2=4.337*10^10
Work= TME2-TME1=3.92*10^9
webassign says I'm wrong. Is my equation for either KE or potential energy incorrrect? Any help is appreciated.

Are you using a negative for U ?

sure am

Sorry for replying late, I have a final for this intro mechanics tomorrow morning :)
This is the way i did it :

E1 (energy at lower orbit) = -GmM/2r1 where r1 is the radius of Mars + 1000 km
E2 (energy at higher orbit)= -GmM/2r2 , r2 is the radius or Mars + 1000 km

m is 2700 kg
M is mass of Mars.

E2-E1 = GmM/2 (1/r1 - 1/r2) gives 5.33 x 10^9 J

Thanks Ahmadmz, that's what I got too after I corrected my excel spreadsheet, had the wrong equation in for velocity. ( I do all my homework in excel)

## 1. How do satellites orbit Mars?

Satellites orbit Mars in an elliptical path due to the planet's gravitational pull. The satellite is launched at a specific speed and angle to achieve a stable orbit around the planet.

## 2. What factors affect the distance of a satellite orbiting Mars?

The distance of a satellite orbiting Mars can be affected by its speed, the gravitational pull of Mars, and any external forces such as solar wind or atmospheric drag.

## 3. How is the distance of a satellite orbiting Mars changed?

The distance of a satellite orbiting Mars can be changed by adjusting its speed or by using thrusters to alter its trajectory. This can be done to achieve a higher or lower orbit, or to change the satellite's position relative to the planet.

## 4. Why would the distance of a satellite orbiting Mars need to be changed?

The distance of a satellite orbiting Mars may need to be changed in order to maintain a stable orbit, to avoid collisions with other satellites or debris, or to achieve specific scientific or observational objectives.

## 5. How is the work done to change the distance of a satellite orbiting Mars calculated?

The work done to change the distance of a satellite orbiting Mars is calculated using the formula W = F x d, where W is the work done, F is the force applied, and d is the distance moved. The force and distance can be determined by measuring the changes in the satellite's velocity and position relative to Mars.

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