# Universal gravitation

• ookt2c
In summary, a synchronous satellite is put in orbit around Jupiter to study the famous red spot. The satellite must have an altitude that allows it to remain above the same point on Jupiter's equator, and the force of gravity must be equal to the centripetal force.

## Homework Statement

A synchronous satellite, which always remains above the same point on a planet's wquator, is put in orbit around Jupiter to study the famous red spot. Jupiter rotates once every 9.84 h. find the altitude of the satelite

## Homework Equations

jupiter: mass in kg 1.90E27,Mean radius 6.99E7,period of revolutions3.74E8,Mean distance from the sun7.78E11 (t^2/R^3)(S^2/M^3)= 2.97E-19

## The Attempt at a Solution

I don't know where to start , missed a day of class

The force of gravity must be equal to the centripetal force. (But this is true for even if the satellite is not synchronous.)

ookt2c said:

## Homework Statement

A synchronous satellite, which always remains above the same point on a planet's wquator, is put in orbit around Jupiter to study the famous red spot. Jupiter rotates once every 9.84 h. find the altitude of the satelite

## Homework Equations

jupiter: mass in kg 1.90E27,Mean radius 6.99E7,period of revolutions3.74E8,Mean distance from the sun7.78E11 (t^2/R^3)(S^2/M^3)= 2.97E-19

## The Attempt at a Solution

I don't know where to start , missed a day of class

Strictly speaking, this is possible only if the point on th eplanet is at the equator. I don't think that the Red Spot is on th eequator but let's pretend it is.

Then you have to impose that the force of gravity on the satellite is equal to m tiomes the radial acceleration so
$$F_{grav} = m \frac{v^2}{r}$$

where "r" is the distance from the satellite to the center of the planet.