# Gravitation and equilibrium (…and similar problems) [closed]

One problem that I'm having trouble with (as opposed to the other):

The Messenger is a probe that orbits Mercury $700 \rm km$ from the surface. What is the tangential velocity it should be rotating at so that it doesn't precipitate towards the planet, in $\rm m/s$?

Data: Mercury's mass $3,3 \times 10 ^{23} \rm kg$ Diameter: $4870 \rm km$ . Gravitational constant: $G=6,67 \times 10^{-11} \rm m^{3}kg^{-1}s^{-2}$

I assume I need to use the following $$a_{c}=\frac {V^2} r$$

$$F=G\frac{m_1 m_2}{d^2}$$

EDIT:

Solving for $V$ in $$G\frac{{{m_1}{m_2}}}{{{d^2}}} = {m_1}\frac{{{V^2}}}{d}$$ did it.

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## closed as off-topic by David Z♦Nov 14 '13 at 1:12

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The answers to your two questions both come out of the observation that you can not equate force to acceleration. To get them into a form where you can equate them alter the second one to get the acceleration of the satellite due to the planets gravity.

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Should I be using Newton's Second Law? –  Peter Tamaroff Jun 22 '12 at 2:57
Do you know another way? This kind of observation is one of the more useful tools in solving physics problems---especial those asked in school. You have one acceleration and once force, and you say "Aha! Newton had something to say about that. What happens if I ..." With luck it all works out. What you are looking for here is a relationship in which the mass of the orbiter (which you've noted you do not have) does not appear. –  dmckee Jun 22 '12 at 3:01
Right. by the way, this is from an introductory course from an university (a basic common course for the exact sciences and engineering factulty.). –  Peter Tamaroff Jun 22 '12 at 3:04
I got it. Thanks. –  Peter Tamaroff Jun 22 '12 at 3:21