If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.

: If a planet crosses ( or transits ) in front of its parent star's disk, then the observed brightness of the star drops by a small amount.

If a planet orbits one member of a binary star system, then an uppercase letter for the star will be followed by a lowercase letter for the planet.

If the heavier body is much more massive than the smaller, as for a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate and convenient to describe the motion in a coordinate system that is centered on the heavier body, and we say that the lighter body is in orbit around the heavier.

If a planet is sufficiently massive, the water on it may be solid even at high temperatures, because of the high pressure caused by gravity, as it was observed on exoplanets Gliese 436 b and GJ 1214 b.

If ranked today, the United Arab Republic would be the 25th largest nation on the planet ( Egypt is 30th and Syria is 88th ).

If an instantaneous centripetal force ( red arrow ) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same.

If such a planet actually existed, according to present scientific cosmology, it would be permanently hidden behind the sun but nevertheless detectable from Earth, because of its gravitational influence upon the other planets of the Solar System.

If the orbit is almost edge-on, then the planet can be seen transiting its star.

If not quite a daughter of the soil, she was a granddaughter of it, and her concern for our planet led her to become an environmentalist, indeed the first female environmentalist to achieve such resounding political success.

' If we can get this done, this is going to be the fucking coolest game that the planet Earth has ever fucking seen in its entire history!

Translating this analogy into space, then, a " stationary " observer sees a planet moving left at speed U and a spaceship moving right at speed v. If the spaceship has the proper trajectory, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction ( to the left ).

If the spacecraft's purpose is only to fly by the inner planet, then there is typically no need to slow the spacecraft.

If the eccentricity was actually this high, the planet would pass through the asteroid belt and clear it out within about ten thousand years.

If a large amount of energy is transmitted, it could heat the surface of the planet to an uninhabitable temperature.

Al Gore has argued " If you're a young person looking at the future of this planet and looking at what is being done right now, and not done, I believe we have reached the stage where it is time for civil disobedience to prevent the construction of new coal plants that do not have carbon capture and sequestration.

If the resistance at both wheels is equal, the planet gear revolves without spinning about its own axis, and both wheels turn at the same rate.

If Epsilon Eridani has an Oort cloud, Luyten 726-8 could gravitationally perturb some of the comets with long orbital periods.

If the belt has existed for longer than this period, which appears likely, it imposes an upper limit on Epsilon Eridani b's eccentricity of about 0. 10 – 0. 15.

If the latter star is gravitationally bound to Epsilon Cygni A, then they are currently separated by 1700 AU or more, and have an orbital period of at least 50, 000 years.

If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.

* If the operation is associative, ( ab ) c = a ( bc ), then the value depends only on the tuple ( a, b, c ).

If c is another common divisor of a and b, then c also divides as + bt

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

If a and b are coprime and a divides the product bc, then a divides c. This can be viewed as a generalization of Euclid's lemma.

If vectors a and b are orthogonal, then and:

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

Linear Diophantine equations take the form ax + by = c. If c is the greatest common divisor of a and b then this is Bézout's identity, and the equation has an infinite number of solutions.

It follows that there are also infinitely many solutions if c is a multiple of the greatest common divisor of a and b. If c is not a multiple of the greatest common divisor of a and b, then the Diophantine equation ax + by = c has no solutions.

:“ If an integer n is greater than 2, then has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain .”

If f is a surjection and a ~ b ↔ f ( a ) = f ( b ), then g is a bijection.

If ~ and ≈ are two equivalence relations on the same set S, and a ~ b implies a ≈ b for all a, b ∈ S, then ≈ is said to be a coarser relation than ~, and ~ is a finer relation than ≈.

Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.

* If < math > a < b </ math > and < math > b < c </ math > then < math > a < c </ math >;

* If < math > a < b </ math > and < math > c < d </ math > then < math > a + c < b + d </ math >;

* If < math > a < b </ math > and then < math > ac < bc </ math >;

* If < math > a < b </ math > and < math > c < 0 </ math > then < math > bc < ac </ math >.

*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.

If this be true, the possibility exists that an occlusive lesion of the bronchial arteries might cause widespread degeneration of supportive tissue similar to that seen in generalized emphysema.

If we cannot make explicit choices, how do we know that our set exists?

Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If community exists, both freedom and security may exist as well.

* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.

If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

If the limit exists, then f is differentiable at a.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If a vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

If total cash available is less than cash needs, a deficiency exists.

If K is a subset of ker ( f ) then there exists a unique homomorphism h: G / K → H such that f = h φ.

If it exists, the graviton is expected to be massless ( because the gravitational force appears to have unlimited range ) and must be a spin 2 boson.

If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.

If there exists an isomorphism between two groups, then the groups are called isomorphic.

If God exists in the understanding, we could imagine Him to be greater by existing in reality.

If such a function exists, we say X and Y are homeomorphic.

* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).

* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).

If the limit exists, we say that ƒ is complex-differentiable at the point z < sub > 0 </ sub >.

If an inverse function exists for a given function ƒ, it is unique: it must be the inverse relation.