Some Physic Questions

[nokhin12]

Suppose that a satellite in a circular orbit at a height of 2.00*10^6m above earth's surface. what is the speed of a satellite in this orbit?

A. 8.31*10^1

B. 6.90*10^3

C. 4.76*10^7

D. 9.62*10^4

 

 

In the absence of air resistance, the least speed which a body must be projected vertically upward from the earth's surface if it is to reach an altitude of 800km is...

A. ~3.92*10^9

B. ~6.26*10^4

C. ~1.10*10^4

D. ~1.21*10^8

 

i couldn't solve these questions...would someone please help me?

ps: Earth's mass = 5.98*10^24

Earth's radius = 6.38*10^6

[Qfwfq]

I suppose your figure for Earth's mass is in kilogrammes, I recognize the radius as being in metres. You also need to look up the universal constant of gravitation, G, preferrably in SI units. It could also be derived by knowing the mass and radius and the acceleration of gravity, g, here at the surface, which is about 9.8 in SI units (metres per second-squared):

 

g = G times M divided by R-square

 

from which you get that G is Earth's mass divided by its radius squared, also divided by g.

 

The second question is easier if you see it as kinetic energy needed to reach that altitude. You don't need to know the body's mass, think of the energy as being "for each kg". The necessary energy is the increase in potential energy when rising to that altitude, in joule/kg it is approximately given by g*8*10^5 but it will be somewhat less because g decreases with altitude. From this you can get the velocity by inverting the kinetic energy formula: E = m*v^2/2, so you'll have to take a square root. If you need the increase of potential energy more exactly, use:

 

GM/R - GM/(R + 800km) equivalent to: GM*800km/(R * (R + 800km))

 

giving some 11% off of the above approximation. You might notice that, in the potential formula, the radius in the denominator is not squared as it is in the formula for acceleration.

 

For the first question you can take the acceleration for R = 8.38*10^6 and equate it to the centripetal acceleration of a circular motion having the same radius and velocity v:

 

a = v^2/R

 

Factoring out an R from both sides of the equation, we derive v as 10^-3 times the square root of GM/8.38