# Homework Help: Satellite synchronous to Venus' rotation

1. Jan 30, 2006

### endeavor

Venus has a rotational period of 243 days. What would be the altitude of a syncom satellite for this planet?

I am pretty sure a syncom satellite is a satellite that orbits synchronously to the rotation of the planet.

I don't know how to solve this problem... help

2. Jan 30, 2006

### Staff: Mentor

Think about what things affect how long it takes a satellite to go around in an orbit. And think about the basics of uniform central motion (something going in a circular path). What is the centripital (sp?) acceleration that causes a mass to go around in a circle? How is that centripital acceleration related to the speed of the mass? Now what is generating that force in the case of a satellite? What about Venus affects the centripital acceleration of the satellite?

3. Jan 31, 2006

### endeavor

ac = v2/(RV + h)
but i don't know ac, v, or h...
v = squareroot of (G * MV / (RV + h))
but i still don't know v or h...

I found that the distance from venus to the sun is 108.2 * 10^9 m, so I figured that's 3.0 * 10^9 m/day. That means every day venus travels 3.0 * 10^9 m. Therefore the circumference of venus is 3.0 * 10^9 m? But that's not right....

I'm still not sure how I'm supposed to solve this...

4. Jan 31, 2006

### SpaceTiger

Staff Emeritus
How might one express the velocity of the satellite in terms of the radius of the orbit and the period?

Hint: What is the shape of the orbit have to be for it to be synchronous? What does this say about how the satellite's speed changes throughout its orbit?

5. Jan 31, 2006

### endeavor

v = (2pi * r)/ T, where T is the period

I have
r = 6052000m + h, where h is the altitude
T=?
To find h, I would have to know v already...

The satellite has to orbit in a circle, and therefore it's speed doesn't change.

6. Jan 31, 2006

### Smilecdl

You know T it is defined in your question...for the Earth T would be 24 hours so what is it for Venus? [Don't forget to change you units to seconds when doing the final calculation]

7. Jan 31, 2006

### SpaceTiger

Staff Emeritus
Good, and what is the other condition for it to be synchronous?

8. Jan 31, 2006

### endeavor

Okay, I finally got the right answer...
I thought 243 days meant that Venus has 243 days in its path around the sun.
Venus and the satellite have to have the same angular speed.
w=v2/(r + h)
I also have the equation for the speed of a satellite:
v2=square root of (GMV/(r + h))

Solving for the two unknowns, v2 and h, I get h = 1.53 * 10^9 m, which is the correct answer.

Thanks for all the great help! I really appreciate it!

9. Oct 28, 2009

### physhater

Sorry, can you explain how you solved for v and then for h? I can see how it would be easy solving for the altitude once you know the v, but I don't know how to get to that.