Centripetal forces and satellites

[supmiller]

Hi I am kind of new to the forum nice to be here! here is my question.

Homework Statement

A satellite is kept in a circular orbit 300km above the surface of the Earth by the force of gravity. At this altitude the acceleration due to gravity is 8.9 m/s. The radius of the Earth is 6.4*10^6m

a) calculate the period of the satellite

b) calculate the speed of the satellite

Homework Equations

Ac=(4(Pi^2)(r))/(T^2)

Where ac is the acceleration
T is the period
r is the radius

V=(2(pi)r)/(T)

The Attempt at a Solution

a)

Using the first equation listed

T= (2(pi))(r/ac)^(1/2)
r=(6.4*10^6)+(300km)(1000m/1km)
ac=8.9m/s

T=5451.6 seconds

b) Using our known T,
V=(2Pi)(6700000)/(5451.6)
V=7722 m/s

Thanks in advance, I feel I may not have the concept down well enough and this may not be the way to do it.

 

[PhanthomJay]

That looks right to me. Welcome to PF as a poster!

 

[c03rcion]

Hi I am kind of new to the forum nice to be here! here is my question.

Homework Statement

A satellite is kept in a circular orbit 300km above the surface of the Earth by the force of gravity. At this altitude the acceleration due to gravity is 8.9 m/s. The radius of the Earth is 6.4*10^6m

a) calculate the period of the satellite

b) calculate the speed of the satellite

Homework Equations

Ac=(4(Pi^2)(r))/(T^2)

Where ac is the acceleration
T is the period
r is the radius

V=(2(pi)r)/(T)

The Attempt at a Solution

a)

Using the first equation listed

T= (2(pi))(r/ac)^(1/2)
r=(6.4*10^6)+(300km)(1000m/1km)
ac=8.9m/s

T=5451.6 seconds

b) Using our known T,
V=(2Pi)(6700000)/(5451.6)
V=7722 m/s

Thanks in advance, I feel I may not have the concept down well enough and this may not be the way to do it.

** r = radius
r = R_E + h = (6.4*10^6m + 300,000m) = 6.7x10^6

**C = Circumference
C=2(PI)r

T=period
T=C/v

**for circular motion there are 2 components of acceleration, radial acceleration and tangential acceleration. the radial (centripetal acceleration) is shown:

A_r=(mv²)/r

**because gravity from the Earth is causing the satellite to undergo centripetal acceleration:

mg = (mv²)/r

**the masses of the satellite cancel to show the speed of the satellite:

(rg)^1/2=v

v = 7722 m/s

** the period
T = 2(PI)r/v = 5448s

Based on what I got, I would say you did a good job!