Calculating Orbit Parameters Given Perigee Velocity and Period

[dorai007]

Hi guys,

i can't seem to find the answer .

A satellite in Earth orbit has a perigee velocity of 8 km=s and period of 2 hours. From this information,
determine all the orbit parameters that you can. From those parameters, determine its altitude at perigee
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my vp=8km/sec
T=7200sec
Vp=sqrt(GM/r)---is this right and is r =rp?





how do i calculate my semi major axis? is it from kepler's 3rd law? I am stuck at finding rp and eccenctricity and I've been going at this for hours without proper examples in books/online.

Someone please help!

 

[D H]

Vp=sqrt(GM/r)---is this right and is r =rp?

That equation is valid only for circular orbits. The vis viva equation provides a more general answer:

$$\frac{v^2}{GM} = \frac 2 r - \frac 1 a$$

how do i calculate my semi major axis? is it from kepler's 3rd law?

Correct. So show some work so we can help you out a bit.

 

[dorai007]

but if its vis viva will my eccentricity value be more than 0.2..thats the value I am getting, this is how I am doing my calculations

1) equation 1 : mag(h)=mag(rp)*mag(v)
equation 2: mag(rp)= [mag(h)^2/GM]/(1+ecos(v) - trajectory eqn
equation 3: T= 2phi/sqrt(GM) * (mag(h))^3/2

i am to solve 3 unknowns mag(h),rp and e by simultaneous eqns by substituting all the equations into one another.

ive done it a couple of times, either I am getting a negative value for e(-0.1) which shldnt be the case.

But my qn here is. if v=8000m/sec what is mag(v)? and in this case will a=mag(h) ?

 

[D H]

but if its vis viva will my eccentricity value be more than 0.2..thats the value I am getting,

Then you are doing it wrong. The eccentricity is less than 0.2. Show your work.

this is how I am doing my calculations

1) equation 1 : mag(h)=mag(rp)*mag(v)
equation 2: mag(rp)= [mag(h)^2/GM]/(1+ecos(v) - trajectory eqn
equation 3: T= 2phi/sqrt(GM) * (mag(h))^3/2

Your equation 1 is only valid for circular orbits, and for elliptical orbits at perifocus and apofocus. (Since the given data point is perigee, this equation is okay here.) Your equation 3 however is only valid for circular orbits.

Try finding a formula that relates semi-major axis (rather than specific angular momentum) to the period.

But my qn here is. if v=8000m/sec what is mag(v)? and in this case will a=mag(h) ?

The magnitude of the velocity vector is of course 8000m/s. As far as a=mag(h), no. Look at the units. Specific angular momentum(h) has units of length²/time. Semi-major axis (a) has units of length.

 

[pmacias]

I would suggest using the following equations to calculate the orbit parameters:

1) Semi-major axis (a) can be calculated using Kepler's Third Law: a = (GM*T^2/4π^2)^(1/3), where G is the gravitational constant (6.67408 × 10^-11 m^3 kg^-1 s^-2), M is the mass of the Earth (5.972 × 10^24 kg), and T is the period in seconds.

2) Perigee distance (rp) can be calculated using the equation: rp = a(1-e), where e is the eccentricity of the orbit. The eccentricity can be found by using the equation: e = (Vp^2*a)/GM - 1, where Vp is the perigee velocity.

3) Altitude at perigee can be calculated by subtracting the radius of the Earth (6371 km) from the perigee distance (rp).

I would also recommend checking your calculations with sample problems or consulting with a colleague or mentor for assistance. It's important to have a solid understanding of the equations and their applications in order to accurately calculate the orbit parameters. Good luck!