Question

satellites and orbits

Answer 1

if a new satellite is placed in a circular orbit at a distance of\[\left| r_2 \right|=4\left| r_1 \right|\]around the same planet what is the ratio\[\frac{v_1}{v_2}\]between the speed of the first satellite and the speed of the new satellite?

Answer 2

the choices are...
A. (2)^(1/2)
B. 1/[(2)^(1/2)]
C. 2
D. 4

Answer 3

i'm thinking that since it's further out by 4/1 the speed will also be 4/1 so i'm thinking he answer is 4?

Answer 4

@surry99

Answer 5

Hint: What are the forces acting on the satellite? There are two and they are equivalent.

Answer 6

gravity and acceleration?

Answer 7

gravitation (Newtons universal law of gravitation) and the centripetal force

Answer 8

Equate the two , then simplify and you will see the relationship between v and r.

Answer 9

I think answer is C:

1) Formula
distance[d]= velocity[V] . time[T]
V=d/T

2) Time
Do you remember Kepler's laws?
\[\frac{ r _{1} ^{3} }{ r _{2}^{3} } = \frac{ T _{1} ^{2} }{ T _{2}^{2} }\]
Lets say r1=1, r2=4 --> (T1/T2)^2 = 1/64 --> T1=1, T2=8

3)Orbit Distance = 2.pi.r

4) Let's put all these in formula

V1 = 2.pi.r1 / T1 --> V1 = 2. pi .1 / 1 --> V1= 2pi

V2 = 2.pi.r2 / T2 --> V2 = 2. pi .4 / 8 --> V2 = pi

5) Result: V1 / V2 = 2pi / pi = 2