- #1

songoku

- 2,328

- 337

- Homework Statement
- A satellite is orbiting earth. The satellite has orbital velocity of 5.9 km/s. If the minimum velocity for the satellite to escape earth is 14.6 km/s, what is the mass of the satellite if the satellite is located 3200 km above earth’s surface?

- Relevant Equations
- ##F=m \frac{v^2}{r}##

##F=G\frac{m_1 . m_2}{r^2}##

##KE=\frac 1 2 mv^2##

##GPE=-G\frac{m_1.m_2}{r}##

I am not really sure what to do to find the mass of satellite.

Equation for orbital speed:

$$m \frac{v^2}{r}=G\frac{m_1 . m_2}{r^2}$$

$$v_{orbital}=\sqrt{\frac{GM}{r}}$$

Equation for escape speed:

$$KE_1+GPE_1=KE_2+GPE_2$$

I tried to take position 1 as the position where the satellite orbits and position 2 is at infinity (where both KE and GPE are zero) but I can't find the mass of the satellite.

How to approach this question? Thanks

Equation for orbital speed:

$$m \frac{v^2}{r}=G\frac{m_1 . m_2}{r^2}$$

$$v_{orbital}=\sqrt{\frac{GM}{r}}$$

Equation for escape speed:

$$KE_1+GPE_1=KE_2+GPE_2$$

I tried to take position 1 as the position where the satellite orbits and position 2 is at infinity (where both KE and GPE are zero) but I can't find the mass of the satellite.

How to approach this question? Thanks