A satellite orbits the Earth with a radius of 7000km. The acceleration of gravity at this distance=8.17m/s/s.
How do I find the velocity of the satellite? I'm really struggling with finding the correct formula. I know the answer but can't figure out how to get there.
Thanks if anyone can help.
gravity is providing the centripetal force (keeping the satellite on a circular path)
a = v² / r
you have a and r, just make the units consistent (a to km OR r to m)
Sorry, I don't understatnd, and the answer doesnt compute to what is considered correct.
a=v^2/r where r is the distance from center Earth (re+altitude). solve for velocity
Thank you
To find the velocity of a satellite orbiting the Earth, you can use the formula for centripetal acceleration. The centripetal acceleration of an object in circular motion can be calculated using the formula:
a = (v^2) / r
Where:
a = acceleration
v = velocity
r = radius or distance from the center of the orbit
In this case, you are given the acceleration of gravity (g) at this distance, which is acting as the centripetal acceleration. So, you can rewrite the formula as:
g = (v^2) / r
To find the velocity (v), rearrange the formula to solve for it:
v = sqrt(g * r)
Now you can substitute the given values into the formula and calculate the velocity:
v = sqrt(8.17 m/s^2 * 7000 km)
Notice that the radius given is in kilometers, while the acceleration is in meters per second squared. It is important to have consistent units in calculations. So, convert 7000 km to meters by multiplying it by 1000:
v = sqrt(8.17 m/s^2 * 7000 km * 1000)
v = sqrt(8.17 m/s^2 * 7,000,000 m^2/s^2)
v = sqrt(56,989,000 m^2/s^2)
v ≈ 7569 m/s
Therefore, the velocity of the satellite is approximately 7569 m/s.