How Do You Calculate Orbital Dynamics for a Satellite Around Planet X?

[thelightsare]

Homework Statement

Planet X has a mass of 6.42x10^20 kg and a radius of 2400km. A satellite with a mass of 1500kg is in orbit around Planet X at an altitude of 300km.
a) what is the Force of Gravity?
b) What is the acceleration of the satellite while in orbit?
c) Find the speed of the satellite in orbit.
d) Find the period of the satellite.

Homework Equations

F = GMm/r^2, maybe f=ma , a = v^2/r?, T= 2 pi r/v

The Attempt at a Solution

a)
F=GMm/r^2
F=6.67e-11*6.42e23*2000/(3400+300)^2
F$$\approx$$6.26e9 N ?

b) very unsure but can you use
f=ma
6.26e9 N=2000a
and solve for a or is tht wrong? I was also maybe thingking of using

c) v = ?
could you use a = v^2/r
a(take answer from b) = v^2/(3400+300) and solve for v
or is this the wrong equation or wrong values?

d)T= 2 pi r/v
T = 2 pi (3400+300)/v(answer from c) ?

Thanks!

 

[ehild]

Your method is correct, but the numbers you plugged in for the masses and radius of the planet do not much with the data given.

ehild

 

[thelightsare]

Your method is correct, but the numbers you plugged in for the masses and radius of the planet do not much with the data given.

ehild

I always have a problem telling which data to use. Any hints or suggestions?

 

[gneill]

I always have a problem telling which data to use. Any hints or suggestions?

Seriously? How about reading the question carefully, using the data that's provided, and checking your figures?

There is no magic formula to help with that!

 

[thelightsare]

Seriously? How about reading the question carefully, using the data that's provided, and checking your figures?

There is no magic formula to help with that!

I just really have trouble deciding which mass to use and wether "r" would mean to use the dist. between objects or the radius. I really really really want to understand and would love any help! Also, how do u check ur answers? It seems like valuable information to know.

 

[ehild]

Read the text of the problem and compare with the data you used when calculating the force: the mass of the planet is 6.42x10^20 kg. It is M. You substituted 6.42x10^23 kg for M. The mass of the satellite is 1500 kg. You substituted 2000 kg for m. The radius of the planet is 2400 m. You plug in 3400 m. ehild

 

[thelightsare]

Read the text of the problem and compare with the data you used when calculating the force: the mass of the planet is 6.42x10^20 kg. It is M. You substituted 6.42x10^23 kg for M. The mass of the satellite is 1500 kg. You substituted 2000 kg for m. The radius of the planet is 2400 m. You plug in 3400 m.


ehild

Oh! THank you so much!

 

[thelightsare]

One quick last question. For a = v^2/r and T= 2 pi r/v would r =2400+300 or just 2400?

 

[ehild]

r=2700 km

ehild

 

[thelightsare]

r=2700 km

ehild

Great! Thanks so much